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Showing papers on "Quantum geometry published in 2012"


Book
05 Feb 2012
TL;DR: A comprehensive account of local quantum physics understood as the synthesis of quantum theory with the principle of locality is given in this paper, which describes both the physical concepts and the mathematical structures and their consequences.
Abstract: This textbook gives a comprehensive account of local quantum physics understood as the synthesis of quantum theory with the principle of locality Centered on the algebraic approach, it describes both the physical concepts and the mathematical structures and their consequences These include the emergence of the particle picture, general collision theory covering the cases of massless particles and infraparticles, the analysis of possible charge structures and exchange symmetries including braid group statistics Thermal states of an unbounded medium and local equilibrium are discussed in detail The author describes both the ideas and to give a critical assessment of future perspectives

1,116 citations


Journal ArticleDOI
TL;DR: In this paper, a generalized notion of holography inspired by holographic dualities in quantum gravity is proposed. The generalization is based upon organizing information in a quantum state in terms of scale and defining a higher-dimensional geometry from this structure.
Abstract: We show how recent progress in real space renormalization group methods can be used to define a generalized notion of holography inspired by holographic dualities in quantum gravity. The generalization is based upon organizing information in a quantum state in terms of scale and defining a higher-dimensional geometry from this structure. While states with a finite correlation length typically give simple geometries, the state at a quantum critical point gives a discrete version of anti-de Sitter space. Some finite temperature quantum states include black hole-like objects. The gross features of equal time correlation functions are also reproduced.

883 citations


Journal ArticleDOI
TL;DR: In this article, a quantum optical control and readout of a quantum oscillator with a mass close to the Planck mass is used to explore possible deviations from the quantum commutation relation.
Abstract: One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Researches are developing various approaches towards such a theory of quantum gravity, but a major hindrance is the lack of experimental evidence of quantum gravitational effects. Yet, the quantization of space-time itself can have experimental implications: the existence of a minimal length scale is widely expected to result in a modification of the Heisenberg uncertainty relation. Here we introduce a scheme to experimentally test this conjecture by probing directly the canonical commutation relation of the center-of-mass mode of a mechanical oscillator with a mass close to the Planck mass. Our protocol utilizes quantum optical control and readout of the mechanical system to probe possible deviations from the quantum commutation relation even at the Planck scale. We show that the scheme is within reach of current technology. It thus opens a feasible route for table-top experiments to explore possible quantum gravitational phenomena.

549 citations


Journal ArticleDOI
TL;DR: The causal dynamical triangulations (CDT) as mentioned in this paper is a formalism of a non-perturbative quantum field theory of gravity via a lattice regularization, and represented as a sum over spacetime histories.

464 citations


MonographDOI
01 Nov 2012
TL;DR: Weinberg as discussed by the authors provides a concise introduction to modern quantum mechanics, in this fully updated second edition of his successful textbook, including six brand new sections covering key topics such as the rigid rotator and quantum key distribution, as well as major additions to existing topics throughout.
Abstract: Nobel Laureate Steven Weinberg combines exceptional physical insight with his gift for clear exposition, to provide a concise introduction to modern quantum mechanics, in this fully updated second edition of his successful textbook. Now including six brand new sections covering key topics such as the rigid rotator and quantum key distribution, as well as major additions to existing topics throughout, this revised edition is ideally suited to a one-year graduate course or as a reference for researchers. Beginning with a review of the history of quantum mechanics and an account of classic solutions of the Schrodinger equation, before quantum mechanics is developed in a modern Hilbert space approach, Weinberg uses his remarkable expertise to elucidate topics such as Bloch waves and band structure, the Wigner–Eckart theorem, magic numbers, isospin symmetry, and general scattering theory. Problems are included at the ends of chapters, with solutions available for instructors at www.cambridge.org/9781107111660.

283 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider branes in refined topological strings and show that their wave-functions satisfy a Schrodinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description.
Abstract: We consider branes in refined topological strings We argue that their wave-functions satisfy a Schrodinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description Furthermore, in the limit where one of the equivariant rotations approaches zero, the brane partition function satisfies a time-independent Schrodinger equation We use this observation, as well as the back reaction of the brane on the closed string geometry, to offer an explanation of the connection between integrable systems and N = 2 gauge systems in four dimensions observed by Nekrasov and Shatashvili

270 citations


Journal ArticleDOI
TL;DR: In this article, a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects.
Abstract: Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 m (Dimopoulos 2007 Phys. Rev. Lett. 98 111102; 2008 Phys. Rev. D 78 042003). In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ~10−20 m, up to that of hundreds of kilometres (Ursin et al 2007 Nature Phys. 3 481–6). Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable.

186 citations


Journal ArticleDOI
TL;DR: In this paper, the authors explore the idea that quantum mechanics and unitarity are fundamental principles, but at the price of familiar locality, and suggest a general framework in which to seek a consistent description of quantum gravity, and approximate emergence of spacetime.
Abstract: The unitary crisis for black holes indicates an apparent need to modify local quantum field theory. This paper explores the idea that quantum mechanics and, in particular, unitarity are fundamental principles, but at the price of familiar locality. Thus, one should seek to parameterize unitary evolution, extending the field theory description of black holes, such that their quantum information is transferred to the external state. This discussion is set in a broader framework of unitary evolution acting on Hilbert spaces comprising subsystems. Here, various constraints can be placed on the dynamics, based on quantum information-theoretic and other general physical considerations, and one can seek to describe dynamics with minimal departure from field theory. While usual spacetime locality may not be a precise concept in quantum gravity, approximate locality seems an important ingredient in physics. In such a Hilbert-space approach an apparently coarser form of localization can be described in terms of tensor decompositions of the Hilbert space of the complete system. This suggests a general framework in which to seek a consistent description of quantum gravity, and approximate emergence of spacetime. Other possible aspects of such a framework---in particular, symmetries---are briefly discussed.

154 citations


Journal ArticleDOI
TL;DR: In this paper, the authors extend classical constructions to canonical quantum gravity and apply them to model systems as well as general metrics, with the following conclusions: Dispersion relations of matter and gravitational waves are deformed in related ways, ensuring a consistent realization of causality.
Abstract: Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to effective constraints of canonical quantum gravity and applied to model systems as well as general metrics, with the following conclusions: (i) Dispersion relations of matter and gravitational waves are deformed in related ways, ensuring a consistent realization of causality. (ii) Inverse-triad corrections modify the classical action in a way clearly distinguishable from curvature effects. In particular, these corrections can be significantly larger than often expected for standard quantum-gravity phenomena. (iii) Finally, holonomy corrections in high-curvature regimes do not signal the evolution from collapse to expansion in a "bounce," but rather the emergence of the universe from Euclidean space at high density. This new version of signature-change cosmology suggests a natural way of posing initial conditions, and a solution to the entropy problem.

139 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of the underlying quantum geometry in loop quantum cosmology on spacetime curvature invariants and the extendibility of geodesics in the Bianchi-I model for matter with a vanishing anisotropic stress were investigated.
Abstract: We investigate the effects of the underlying quantum geometry in loop quantum cosmology on spacetime curvature invariants and the extendibility of geodesics in the Bianchi-I model for matter with a vanishing anisotropic stress. Using the effective Hamiltonian approach, we find that even though quantum geometric effects bound the energy density and expansion and shear scalars, divergences of curvature invariants are potentially possible under special conditions. However, as in the isotropic models in LQC, these do not necessarily imply a physical singularity. Analysis of geodesics and strength of such singular events, point towards a general resolution of all known types of strong singularities. We illustrate these results for the case of a perfect fluid with an arbitrary finite equation of state $w > -1$, and show that curvature invariants turn out to be bounded, leading to the absence of strong singularities. Unlike classical theory, geodesic evolution does not break down. We also discuss possible generalizations of sudden singularities which may arise at a non-vanishing volume, causing a divergence in curvature invariants. Such finite volume singularities are shown to be weak and harmless.

110 citations


Journal ArticleDOI
TL;DR: In this paper, uncertainty relations for single-particle quantum mechanics are derived by a moment expansion of states for quantum systems with a discrete coordinate and, correspondingly, a periodic momentum, with some similarities but also key differences to what is often assumed in this context.
Abstract: Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on nontrivial space-time structures such as a fundamental discreteness of space, a universal band limit or an irreducible extendedness of elementary particles. In this article, uncertainty relations for single-particle quantum mechanics are derived by a moment expansion of states for quantum systems with a discrete coordinate and, correspondingly, a periodic momentum. Corrections to standard uncertainty relations are found, with some similarities but also key differences to what is often assumed in this context. The relations provided can be applied to discrete models of matter or space-time, including loop quantum cosmology.

Journal ArticleDOI
TL;DR: In this paper, a theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, and the amplitude of the effect in physical units is predicted with no parameters, by equating the number of degrees of freedom of position wave functions on a 2D space-like surface with the entropy density of a black hole event horizon.
Abstract: A theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, ${t}_{P}$. Departures from classical world lines in flat spacetime are described by Planckian noncommuting operators for position in different directions, as defined by interactions with null waves. The resulting evolution of position wave functions in two dimensions displays a new kind of directionally coherent quantum noise of transverse position. The amplitude of the effect in physical units is predicted with no parameters, by equating the number of degrees of freedom of position wave functions on a 2D space-like surface with the entropy density of a black hole event horizon of the same area. In a region of size $L$, the effect resembles spatially and directionally coherent random transverse shear deformations on time scale $\ensuremath{\approx}L/c$ with typical amplitude $\ensuremath{\approx}\sqrt{c{t}_{P}L}$. This quantum-geometrical ``holographic noise'' in position is not describable as fluctuations of a quantized metric, or as any kind of fluctuation, dispersion or propagation effect in quantum fields. In a Michelson interferometer the effect appears as noise that resembles a random Planckian walk of the beam splitter for durations up to the light-crossing time. Signal spectra and correlation functions in interferometers are derived, and predicted to be comparable with the sensitivities of current and planned experiments. It is proposed that nearly colocated Michelson interferometers of laboratory scale, cross-correlated at high frequency, can test the Planckian noise prediction with current technology.

Book ChapterDOI
TL;DR: The opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011 was based on the opening lecture.
Abstract: This article is based on the opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011. The goal of the lecture was to present a broad perspective on loop quantum gravity for young researchers. The first part is addressed to beginning students and the second to young researchers who are already working in quantum gravity.

Journal ArticleDOI
TL;DR: In this paper, a holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base.
Abstract: We study the quantum geometry of the class of Calabi-Yau threefolds, which are elliptic brations over a two-dimensional toric base. A holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base. T -duality on the bre implies that the topological string free energy also captures the BPSinvariants of D4-branes wrapping the elliptic bre and a class in the base. We verify this proposal by explicit computation of the BPS invariants of 3D4-branes on the rational elliptic surface.


Journal ArticleDOI
TL;DR: In this paper, the authors study the dynamics of the scalar modes of linear perturbations around a flat, homogeneous and isotropic background in loop quantum cosmology and show that the effective scalar and diffeomorphism constraints are preserved by the dynamics.
Abstract: We study the dynamics of the scalar modes of linear perturbations around a flat, homogeneous and isotropic background in loop quantum cosmology. The equations of motion include quantum geometry effects and are expected to hold at all curvature scales so long as the wavelengths of the inhomogeneous modes of interest remain larger than the Planck length. These equations are obtained by including holonomy corrections in an effective Hamiltonian and then using the standard variational principle. We show that the effective scalar and diffeomorphism constraints are preserved by the dynamics. We also make some comments regarding potential inverse triad corrections.

Journal ArticleDOI
TL;DR: The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the nonnegative integers as discussed by the authors.
Abstract: The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the nonnegative integers. Using this method we classify, according to such localization properties, all the quantum walks with one defect at the origin, providing explicit expressions for the asymptotic return probabilities to the origin.

Posted Content
TL;DR: In this article, a holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base.
Abstract: We study the quantum geometry of the class of Calabi-Yau threefolds, which are elliptic fibrations over a two-dimensional toric base. A holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base. T-duality on the fibre implies that the topological string free energy also captures the BPS-invariants of D4-branes wrapping the elliptic fibre and a class in the base. We verify this proposal by explicit computation of the BPS invariants of 3 D4-branes on the rational elliptic surface.

Journal ArticleDOI
TL;DR: In this article, the two-point correlation function is calculated in the Lorentzian EPRL spinfoam model and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of quantum geometry finite and fixed.
Abstract: The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the quantum geometry finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.

Journal ArticleDOI
TL;DR: In this article, the scalar modes of linear perturbations in loop quantum cosmology were studied on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via the standard homogeneous loop physics techniques.
Abstract: We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via the standard homogeneous loop quantum cosmology techniques. The appropriate interactions between nearby cells are included in the Hamiltonian in order to obtain the correct physics. It is shown that the quantum theory is anomaly free: the scalar and diffeomorphism constraint operators weakly commute with the Hamiltonian. Finally, the effective theory encoding the leading order quantum gravity corrections is derived and is shown to give the same holonomy-corrected effective equations that have been obtained in previous studies. Communicated by P R L V Moniz.

Journal ArticleDOI
TL;DR: In this article, a cosmological model derived from Loop Quantum Gravity is presented, which is based on a projection of the kinematical Hilbert space of the full theory down to a subspace representing the proper arena for an inhomogeneous Bianchi I model.
Abstract: We present a new cosmological model derived from Loop Quantum Gravity. The formulation is based on a projection of the kinematical Hilbert space of the full theory down to a subspace representing the proper arena for an inhomogeneous Bianchi I model. This procedure gives a direct link between the full theory and its cosmological sector. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could also shed light on Loop Quantum Cosmology and its relation with the full theory.

Journal Article
TL;DR: In this article, the hierarchical equations of motion (HEOM) approach is considered as a fundamental formalism in quantum mechanics of dissipative and open systems, and numerical results on the 2D spectrum of a model light harvesting antenna system and the quantum transport through Anderson model quantum dots system are presented.
Abstract: In the mesoscopic world the nano-structured environment is not just of quantum in nature but also often nonperturbative and non-Markovian for its influence on the system of primary interest. In this talk, I will discuss the hierarchical equations of motion (HEOM) approach [1–4] that can be considered as a fundamental formalism in quantum mechanics of dissipative and open systems. HEOM is formally equivalent to such as the Feynman-Vernon influence functional and nonequilibrium many-body Green’s function formalisms [5], but numerically more implementable. It provides a unified treatment of various decoherence and quantum transport processes. It renders also a unified view on various existing approximated theories, such as the quantum master equation and stochastic Liouville equation [6], and consequently, often further results in some simple but important modifications to those conventional approximations [7]. I will also discuss about two recent developments, the best/minimum stochastic environment basis set for optimal HEOM construction [8] and the efficient on-the-fly numerical filtering algorithm [9], that significantly enhance the numerical tractability of the exact HEOM dynamics. Numerical results on the 2D spectrum of a model light harvesting antenna system and the quantum transport through Anderson model quantum dots system will be presented.

Journal ArticleDOI
TL;DR: In this article, a general profile of the spectral dimension of the recently introduced multifractional spaces is constructed for the first time, using tools of probability theory and multifractal geometry, and how dimensional flow is controlled by a multiscale fractional diffusion equation, and physically interpreted as a composite stochastic process.
Abstract: The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is controlled by a multiscale fractional diffusion equation, and physically interpreted as a composite stochastic process. The simplest example is a fractional telegraph process, describing quantum spacetimes with a spectral dimension equal to 2 in the ultraviolet and monotonically rising to 4 towards the infrared. The general profile of the spectral dimension of the recently introduced multifractional spaces is constructed for the first time. The spectral properties of effective quantum geometries show that the ultraviolet (UV) finiteness of independent theories of quantum gravity is universally associated with a lower spectral dimension of spacetime (typically, dS ∼ 2) at small scales, while dS ∼ 4 in the infrared (IR). Instances are causal dynamical triangulations (CDT) [1], asymptotic safety (QEG) [2, 3], spin foams [4, 5], noncommutative geometry [6], Hoyrava-Lifshitz gravity [7], and other approaches [8]. The change of dimension with the probed scale is known as dimensional reduction or dimensional flow [9]. Understanding its physical meaning is an important piece of the puzzle of quantum gravity, since multiscale behavior is deeply related to the renormalization properties of these theories. Differential geometry and ordinary calculus, as employed in general relativity and field theory, are inadequate to study this and other properties of quantum spacetimes, and stochastic processes and multifractal geometry can offer powerful tools of analysis and novel insight. While there is the tendency to label all multiscale spaces as “fractal,” the accumulated knowledge from these branches of mathematics permit to make sharper statements about the geometric and physical properties of quantum-gravity models. This philosophy inspired the revisiting of a recent problem, the construction of quantum field theories in fractal spacetimes, under a fresh perspective focused on an effective continuum geometry [10], in particular via the formalism of multifractional spacetimes [11]. After a sketch of the classical situation, we will argue that quantum geometry effectively modifies the diffusion equation. A critical appraisal of the latter will allow us to classify quantum geometries in terms of stochastic processes on one hand, and to get a precise back-up to the notion of “fractal spacetime” on the other hand. The aim is to reexamine the spectral dimension starting from its foundation and provide a general, model-independent and analytic description of dimensional flow, confirmed by quantum-gravity examples. This is possible thanks to the presence of universal features in the flow [12]. For a diffusion process to be meaningful, the solution

Book ChapterDOI
TL;DR: In this article, causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory and the fermionic projector and causal variational principles are recovered.
Abstract: Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and causal variational principles. We review how an effect of spontaneous structure formation gives rise to a topology and a causal structure in space-time. Moreover, we outline how to construct a spin connection and curvature, leading to a proposal for a “quantum geometry” in the Lorentzian setting. We review recent numerical and analytical results on the support of minimizers of causal variational principles which reveal a “quantization effect” resulting in a discreteness of space-time. A brief survey is given on the correspondence to quantum field theory and gauge theories.

Journal ArticleDOI
TL;DR: In this paper, the thermal quantum and total correlations in the anisotropic XY spin chain in transverse field were investigated, and the ability of these measures to estimate the critical point at finite temperature strongly depend on the Hamiltonian's anisotropy parameter.

Journal ArticleDOI
TL;DR: In this article, a general anharmonic oscillator is derived for quantum gravity and cosmology systems, and detailed derivations are presented for systems in quantum physics and quantum computer vision.
Abstract: Quantum-corrected equations of motion generically contain higher time derivatives, computed here in the setting of canonically quantized systems. The main example in which detailed derivations are presented is a general anharmonic oscillator, but conclusions can be drawn also for systems in quantum gravity and cosmology.

Journal ArticleDOI
TL;DR: In this article, the Tannaka-Krein duality theory for quantum homogeneous spaces was applied to the case of the quantum SU(2) groups and the equivariant maps between these spaces can be characterized by certain quadratic equations associated with the braiding on the representations of SUq(2).
Abstract: We apply the Tannaka-Krein duality theory for quantum homogeneous spaces, developed in the first part of this series of papers, to the case of the quantum SU(2) groups. We obtain a classification of their quantum homogeneous spaces in terms of weighted oriented graphs. The equivariant maps between these quantum homogeneous spaces can be characterized by certain quadratic equations associated with the braiding on the representations of SUq(2). We show that, for |q| close to 1, all quantum homogeneous spaces are realized by coideals.

Journal ArticleDOI
TL;DR: In this article, a modification to the standard construction, based on the recently introduced (non-commutative) flux representation, was introduced, and the resulting quantum states have some welcome features, in particular, concerning peakedness properties, when compared to other coherent states in the literature.
Abstract: As part of a wider study of coherent states in (loop) quantum gravity, we introduce a modification to the standard construction, based on the recently introduced (non-commutative) flux representation. The resulting quantum states have some welcome features, in particular, concerning peakedness properties, when compared to other coherent states in the literature.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?Coherent states: mathematical and physical aspects?.

Posted Content
TL;DR: In this paper, it was shown that if each quantum event is associated with a Planck-scale area removed from two-dimensional surfaces in the volume in which the event takes place, then Einstein's equations must hold.
Abstract: In Einstein's gedankenexperiment for measuring space and time, an ensemble of clocks moving through curved spacetime measures geometry by sending signals back and forth, as in the global positioning system (GPS). Combining well-known quantum limits to measurement with the requirement that the energy density of clocks and signals be be no greater than the black hole density leads to the quantum geometric limit: the total number of ticks of clocks and clicks of detectors that can be contained in a four volume of spacetime of radius r and temporal extent t is less than or equal to rt/\pi l_P t_P, where l_P, t_P are the Planck length and time. The quantum geometric limit suggests that each event or `op' that takes place in a four-volume of spacetime is associated with a Planck-scale area. This paper shows that the quantum geometric limit can be used to derive general relativity: if each quantum event is associated with a Planck-scale area removed from two-dimensional surfaces in the volume in which the event takes place, then Einstein's equations must hold.

Journal ArticleDOI
TL;DR: In this paper, the position nonequilibrium correlation function of a quantum Brownian particle with general Gaussian nonfactorizing initial conditions is derived from a generating functional, which is then used to model the dynamics of a particle trapped in a harmonic potential after position measurement.
Abstract: Impurity motion in one-dimensional ultracold quantum liquids confined in an optical trap has attracted much interest recently. As a step towards its full understanding, we construct a generating functional from which we derive the position nonequilibrium correlation function of a quantum Brownian particle with general Gaussian nonfactorizing initial conditions. We investigate the slow dynamics of a particle confined in a harmonic potential after a position measurement; the rapid relaxation of a particle trapped in a harmonic potential after a quantum quench realized as a sudden change in the potential parameters; and the evolution of an impurity in contact with a one-dimensional bosonic quantum gas. We argue that such an impurity--Luttinger-liquid system, which has been recently realized experimentally, admits a simple modeling as quantum Brownian motion in a super-Ohmic bath.