Showing papers on "Quantization (physics) published in 2011"

Search for Majorana fermions in superconductors

Abstract: This is a colloquium-style introduction to the midgap excitations in superconductors known as Majorana fermions. These elusive particles, equal to their own antiparticle, may or may not exist in Nature as elementary building blocks, but in condensed matter they can be constructed out of electron and hole excitations. What is needed is a superconductor to hide the charge difference, and a topological (Berry) phase to eliminate the energy difference from zero-point motion. A pair of widely separated Majorana fermions, bound to magnetic or electrostatic defects, has non-Abelian exchange statistics. A qubit encoded in this Majorana pair is expected to have an unusually long coherence time. We discuss strategies to detect Majorana fermions in a topological superconductor, as well as possible applications in a quantum computer. The status of the experimental search is reviewed. Contents: I. What Are They? (Their origin in particle physics; Their emergence in superconductors; Their potential for quantum computing) II. How to Make Them (Shockley mechanism; Chiral p-wave superconductors; Topological insulators; Semiconductor heterostructures) III. How to Detect Them (Half-integer conductance quantization; Nonlocal tunneling; 4\pi-periodic Josephson effect; Thermal metal-insulator transition) IV. How to Use Them (Topological qubits; Read out; Braiding) V. Outlook on the Experimental Progress [scheduled for vol. 4 of Annual Review of Condensed Matter Physics]

Non-Hermitian Quantum Mechanics

Abstract: Non-Hermitian quantum mechanics (NHQM) is an important alternative to the standard (Hermitian) formalism of quantum mechanics, enabling the solution of otherwise difficult problems. The first book to present this theory, it is useful to advanced graduate students and researchers in physics, chemistry and engineering. NHQM provides powerful numerical and analytical tools for the study of resonance phenomena - perhaps one of the most striking events in nature. It is especially useful for problems whose solutions cause extreme difficulties within the structure of a conventional Hermitian framework. NHQM has applications in a variety of fields, including optics, where the refractive index is complex; quantum field theory, where the parity-time (PT) symmetry properties of the Hamiltonian are investigated; and atomic and molecular physics and electrical engineering, where complex potentials are introduced to simplify numerical calculations.

Quantum Field Theory of Non-equilibrium States

Abstract: Preface 1. Quantum fields 2. Operators on the multi-particle state space 3. Quantum dynamics and Green's functions 4. Non-equilibrium theory 5. Real-time formalism 6. Linear response theory 7. Quantum kinetic equations 8. Non-equilibrium superconductivity 9. Diagrammatics and generating functionals 10. Effective action 11. Disordered conductors 12. Classical statistical dynamics Appendices: A. Path integrals B. Retarded and advanced propagators C. Analytic properties of Green's functions Bibliography Index.

Hall viscosity, orbital spin, and geometry: Paired superfluids and quantum Hall systems

Abstract: The Hall viscosity, a nondissipative transport coefficient analogous to Hall conductivity, is considered for quantum fluids in gapped or topological phases. The relation of the Hall viscosity to the mean orbital spin per particle $\overline{s}$ (discovered in previous work) is elucidated with the help of examples and of the geometry of shear transformations and rotations. For noninteracting particles in a magnetic field, there are several ways to derive the result (even at nonzero temperature), including standard linear response theory. Arguments for the quantization, and the robustness of $\overline{s}$ to small changes in the Hamiltonian that preserve rotational invariance, are given. Numerical calculations of adiabatic transport are performed to check the predictions for quantum Hall systems, with excellent agreement for trial states. The coefficient of ${k}^{4}$ in the static structure factor is also considered and shown to be exactly related to the orbital spin and robust to perturbations in rotation invariant systems.

Finite Quantum Electrodynamics: The Causal Approach

Abstract: Contents: 0. Preliminaries.- 1. Relativistic Quantum Mechanics.- 2. Field Quantization.- 3. Causal Perturbation Theory.- 4. Properties of the S-Matrix.- 5. Other Electromagnetic Couplings.- 6. Epilogue: Non-Abelian Gauge Theories.- Appendices.- Bibliographical Notes.- Subject Index.

The microscopic dynamics of quantum space as a group field theory

Abstract: We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3D Riemannian gravity, and discuss briefly the current status of the 4-dimensional extensions of this construction. We also briefly report on some recent results, concerning both the mathematical definition of GFT models as bona fide field theories, and avenues towards extracting testable physics from them. Introduction The field of non-perturbative and background-independent quantum gravity has progressed considerably over the past few decades [78]. New research directions are being developed, new important developments are taking place in existing approaches, and some of these approaches are converging to one another. As a result, ideas and tools from one become relevant to another, and trigger further progress. The group field theory (GFT) formalism [39, 77, 79] nicely captures this convergence of approaches and ideas. It is a generalization of the much studied matrix models for 2D quantum gravity and string theory [28, 53]. At the same time, it generalizes it, as we are going to explain, by incorporating the insights coming from canonical loop quantum gravity and its covariant spin foam formulation of the dynamics, and so it became an important part of this approach to the quantization of 4D gravity [72, 74, 81, 85]. Furthermore, it is a point of convergence of the same loop quantum gravity approach and of simplicial quantum gravity approaches, like quantum Regge calculus [93] and dynamical triangulations [3, 79], in that the covariant dynamics of the first takes the form, as we are going to see, of simplicial path integrals.

Quantization of Integrable Systems and a 2d/4d Duality

Abstract: We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two dimensions. On the four dimensional side, our main example is N=2 SQCD with gauge group SU(L) and 2L fundamental flavours. Using ideas of Nekrasov and Shatashvili, we argue that the Coulomb branch of this theory provides a quantization of the classical Heisenberg SL(2) spin chain. Agreement with the standard quantization via the Algebraic Bethe Ansatz implies the existence of an isomorphism between the chiral ring of the 4d theory and that of a certain two-dimensional theory. The latter can be understood as the worldvolume theory on a surface operator/vortex string probing the Higgs branch of the same 4d theory. We check the proposed duality by explicit calculation at low orders in the instanton expansion. One striking consequence is that the Seiberg-Witten solution of the 4d theory is captured by a one-loop computation in two dimensions. The duality also has interesting connections with the AGT conjecture, matrix models and topological string theory where it corresponds to a refined version of the geometric transition.

Direct simulation of electron transfer using ring polymer molecular dynamics: Comparison with semiclassical instanton theory and exact quantum methods

Abstract: The use of ring polymer molecular dynamics (RPMD) for the direct simulation of electron transfer (ET) reaction dynamics is analyzed in the context of Marcus theory, semiclassical instanton theory, and exact quantum dynamics approaches. For both fully atomistic and system-bath representations of condensed-phase ET, we demonstrate that RPMD accurately predicts both ET reaction rates and mechanisms throughout the normal and activationless regimes of the thermodynamic driving force. Analysis of the ensemble of reactive RPMD trajectories reveals the solvent reorganization mechanism for ET that is anticipated in the Marcus rate theory, and the accuracy of the RPMD rate calculation is understood in terms of its exact description of statistical fluctuations and its formal connection to semiclassical instanton theory for deep-tunneling processes. In the inverted regime of the thermodynamic driving force, neither RPMD nor a related formulation of semiclassical instanton theory capture the characteristic turnover in the reaction rate; comparison with exact quantum dynamics simulations reveals that these methods provide inadequate quantization of the real-time electronic-state dynamics in the inverted regime.

Shortcomings in the Understanding of why Cosmological Perturbations Look Classical

Abstract: There is a persistent state of confusion regarding the account of the quantum origin of the seeds of cosmological structure during inflation. The issue is the transition from the quantum uncertainties in the homogeneous and isotropic initial state, into the late-time "classical" anisotropies and inhomogeneities. There seems to be a widespread belief that decoherence addresses the issue in a satisfactory way. This view is taken, often implicitly, by most researchers working in the field. This can be seen most clearly in those accounts intended on facing the issue directly. For instance, a recent article [C. Kiefer and D. Polarski, arXiv: 0810.0087] argues just that, and presents a detailed explanation of the justifications. The explicit nature of that account will allow us to discuss the issue in detail. There are, of course, various other works that often indirectly address the issue with similar approaches (see Refs. 2–13). This type of arguments do not only implicitly assume that decoherence offers a satisfactory solution to the measurement problem in quantum mechanics, but also that, in particular, such approach is applicable to these quantum aspects of cosmology. We will review here, why do we, together with various other researchers in the field, consider that this assumption is not correct in general. Moreover as previously discussed in Refs. 22–26, we will argue that the cosmological situation is one where the measurement problem of quantum mechanics appears in a particular exacerbated form, and that, it is this, even sharper conundrum, that should be addressed when dealing with the inflationary account of the origin of the seeds of cosmic structure in the early Universe. We briefly discuss the ideas behind what we feel might be a promising approach to deal with this problem.

Message-passing estimation from quantized samples

Abstract: Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so This paper develops generalized approximate message passing (GAMP) algorithms for minimum mean-squared error estimation of a random vector from quantized linear measurements, notably allowing the linear expansion to be overcomplete or undercomplete and the scalar quantization to be regular or non-regular GAMP is a recently-developed class of algorithms that uses Gaussian approximations in belief propagation and allows arbitrary separable input and output channels Scalar quantization of measurements is incorporated into the output channel formalism, leading to the first tractable and effective method for high-dimensional estimation problems involving non-regular scalar quantization Non-regular quantization is empirically demonstrated to greatly improve rate-distortion performance in some problems with oversampling or with undersampling combined with a sparsity-inducing prior Under the assumption of a Gaussian measurement matrix with iid entries, the asymptotic error performance of GAMP can be accurately predicted and tracked through the state evolution formalism We additionally use state evolution to design MSE-optimal scalar quantizers for GAMP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers

Feynman-Kac-Type Theorems and Gibbs Measures on Path Space: With Applications to Rigorous Quantum Field Theory

Abstract: This text offers a reliable and state-of-the-art introduction to the theory and method of Feynman-Kac formulas approached from three separate branches. These ideas are developed into a synthesis of applications in mathematical physics, principally in models of quantum field theory.Both beginners and experts are addressed, while putting an emphasis on the interdisciplinary character of the book. It offers an introduction to Feynman-Kac formulas. It provides applications to mathematical physics.

Effective approach to the problem of time: general features and examples

Abstract: The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the quantum constrained system can be truncated to finite size and solved by the reduced phase space or gauge-fixing methods. In particular, the classical feasibility of local internal times is directly generalized to quantum systems, overcoming the main difficulties associated with the general problem of time in the semiclassical realm. The key features of local internal times and the procedure of patching global solutions using overlapping intervals of local internal times are described and illustrated by two quantum mechanical examples. Relational evolution in a given choice of internal time is most conveniently described and interpreted in a corresponding choice of gauge at the effective level and changing the internal clock is, therefore, essentially achieved by a gauge transformation. This article complements the conceptual discussion in [M. Bojowald, P. A. H\"ohn, and A. Tsobanjan, Classical Quantum Gravity 28, 035006 (2011).].

Anomalously strong pinning of the filling factor nu=2 in epitaxial graphene

Abstract: We explore the robust quantization of the Hall resistance in epitaxial graphene grown on Si-terminated SiC. Uniquely to this system, the dominance of quantum over classical capacitance in the charge transfer between the substrate and graphene is such that Landau levels (in particular, the one at exactly zero energy) remain completely filled over an extraordinarily broad range of magnetic fields. One important implication of this pinning of the filling factor is that the system can sustain a very high nondissipative current. This makes epitaxial graphene ideally suited for quantum resistance metrology, and we have achieved a precision of 3 parts in 1010 in the Hall resistance-quantization measurements.

Sums over Topological Sectors and Quantization of Fayet-Iliopoulos Parameters

Abstract: In this paper we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories with altered nonperturbative sectors, which were recently used to argue a fractional quantization condition. Nonlinear sigma models with altered nonperturbative sectors are the same as nonlinear sigma models on special stacks known as gerbes. After reviewing the existing results on such theories in two dimensions, we discuss examples of gerby moduli ‘spaces’ appearing in four-dimensional field theory and string compactifications, and the effect of various dualities. We discuss global topological defects arising when a field or string theory moduli space has a gerbe structure. We also outline how to generalize results of Bagger-Witten and more recent authors on quantization issues in supergravities from smooth moduli spaces to smooth moduli stacks, focusing particular attention on stacks that have gerbe structures.

Entanglement between the future and the past in the quantum vacuum.

Abstract: We note that massless fields within the future and past light cone may be quantized as independent systems. We show that the vacuum is an entangled state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. We describe a detector which exhibits a thermal response to the vacuum when switched on at t=0. The feasibility of experimentally detecting this effect is discussed.

Metallic Quantum Well States in Artificial Structures of Strongly Correlated Oxide

Abstract: The quantum confinement of strongly correlated electrons in artificial structures provides a platform for studying the behavior of correlated Fermi-liquid states in reduced dimensions. We report the creation and control of two-dimensional electron-liquid states in ultrathin films of SrVO3 grown on Nb:SrTiO3 substrates, which are artificial oxide structures that can be varied in thickness by single monolayers. Angle-resolved photoemission from the SrVO3/Nb:SrTiO3 samples shows metallic quantum well states that are adequately described by the well-known phase-shift quantization rule. The observed quantum well states in SrVO3 ultrathin films exhibit distinctive features—such as orbital-selective quantization originating from the anisotropic orbital character of the V 3d states and unusual band renormalization of the subbands near the Fermi level—that reflect complex interactions in the quantum well.

Impact of field-induced quantum confinement in tunneling field-effect devices

Abstract: Being the working principle of a tunnel field-effect transistor, band-to-band tunneling is given a rigorous quantum mechanical treatment to incorporate confinement effects, multiple electron and hole valleys, and interactions with phonons. The model reveals that the strong band bending near the gate dielectric, required to create short tunnel paths, results in quantization of the energy bands. Comparison with semiclassical models reveals a big shift in the onset of tunneling. The effective mass difference of the distinct valleys is found to reduce the subthreshold swing steepness.

4-dimensional Spin-foam Model with Quantum Lorentz Group

Abstract: We study the quantum group deformation of the Lorentzian EPRL spin-foam model. The construction uses the harmonic analysis on the quantum Lorentz group. We show that the quantum group spin-foam model so defined is free of the infra-red divergence, thus gives a finite partition function on a fixed triangulation. We expect this quantum group spin-foam model is a spin-foam quantization of discrete gravity with a cosmological constant.

Taking particle physics seriously: A critique of the algebraic approach to quantum field theory

Abstract: I argue against the currently prevalent view that algebraic quantum field theory (AQFT) is the correct framework for philosophy of quantum field theory and that “conventional” quantum field theory (CQFT), of the sort used in mainstream particle physics, is not suitable for foundational study. In doing so, I defend that position that AQFT and CQFT should be understood as rival programs to resolve the mathematical and physical pathologies of renormalization theory, and that CQFT has succeeded in this task and AQFT has failed. I also defend CQFT from recent criticisms made by Doreen Fraser.

A Geometric Construction of the Witten Genus, I

Abstract: I describe how the Witten genus of a complex manifold X can be seen from a rigorous analysis of a certain two-dimensional quantum field theory of maps from a surface to X.

Energy spectrum of the Manning-Rosen potential including centrifugal term solved by exact and proper quantization rules

Abstract: The energy spectrum of the Manning-Rosen potential including centrifugal term in higher dimensions is presented by exact quantization rule approach. The result is compared with that by proper quantization rule method. It is found that the latter is better than that of the exact quantization rule. We find that the interdimensional degeneracy exists for the states in different dimensions. For the special case D = 3, the results agree well with those obtained by other methods.

Loop quantum cosmology of the k = 1 FRW: A tale of two bounces

Abstract: We consider the $k=1$ Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process In spatially nonflat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible Instead, one has to implement the quantum constraints by approximating the connection via open holonomies In the case of flat $k=0$ FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed $k=1$ FRW model they might yield different quantum theories In this manuscript we explore these two quantizations and the different effective descriptions they provide of the bouncing cyclic universe In particular, as we show in detail, the most dramatic difference is that in the theory defined by the new quantization method, there is not one, but two different bounces through which the cyclic universe alternates We show that for a ``large'' universe, these two bounces are very similar and, therefore, practically indistinguishable, approaching the dynamics of the ``curvature-based'' quantum theory

Comprehensive Solution to the Cosmological Constant, Zero-Point Energy, and Quantum Gravity Problems

Abstract: We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.

Influence of electron-acoustic phonon scattering on off-resonant cavity feeding within a strongly coupled quantum-dot cavity system

Abstract: We present a quantum optics approach to describe the influence of electron-acoustic phonon coupling on the emission spectra of a strongly coupled quantum-dot cavity system. Using a canonical Hamiltonian for light quantization and a photon Green function formalism, phonons are included to all orders through the quantum-dot polarizability function obtained within the independent boson model. We derive simple user-friendly analytical expressions for the linear quantum light spectrum, including the influence from both exciton- and cavity-emission decay channels. In the regime of semiconductor cavity QED, we study cavity emission for various exciton-cavity detunings and demonstrate rich spectral asymmetries as well as cavity-mode suppression and enhancement effects. Our technique is nonperturbative and non-Markovian, and can be applied to study photon emission from a wide range of semiconductor quantum-dot structures, including waveguides and coupled cavity arrays. We compare our theory directly to recent and apparently puzzling experimental data for a single site-controlled quantum dot in a photonic crystal cavity and show good agreement as a function of cavity-dot detuning and as a function of temperature.

Relativistic Landau-Aharonov-Casher quantization based on the Lorentz symmetry violation background

Abstract: Based on the discussions about the Aharonov-Casher effect in the Lorentz symmetry violation background, we show that the analogue of the relativistic Landau quantization in the Aharonov-Casher setup can be achieved in the Lorentz-symmetry violation background.

A-polynomial, B-model, and Quantization

Abstract: Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly in a suitable semi-classical limit, as $\hbar \to 0$, and becomes non-commutative or "quantum" away from this limit. For a classical curve defined by the zero locus of a polynomial $A(x,y)$, we provide a construction of its non-commutative counterpart $\hat{A} (\hat x, \hat y)$ using the technique of the topological recursion. This leads to a powerful and systematic algorithm for computing $\hat{A}$ that, surprisingly, turns out to be much simpler than any of the existent methods. In particular, as a bonus feature of our approach comes a curious observation that, for all curves that come from knots or topological strings, their non-commutative counterparts can be determined just from the first few steps of the topological recursion. We also propose a K-theory criterion for a curve to be "quantizable," and then apply our construction to many examples that come from applications to knots, strings, instantons, and random matrices.

The Quantum Hall Effects: Integral and Fractional

Abstract: 1. Quantum Hall Effect: The Basics.- 1.1 Two-Dimensional Electron Gas.- 1.2 Electrons in a Strong Magnetic Field.- 2. Integral Quantum Hall Effect.- 2.1 Experimental Work.- 2.2 Classical Hall Effect.- 2.3 Quantum Mechanical Approach.- 2.4 Integral Quantization: Theoretical Work.- 2.5 Kubo Formula Approach.- 2.6 The Gauge Invariance Approach.- 2.7 The Topological Invariance Approach.- 3. Other Developments.- 3.1 Electron Localization in the Quantum Hall Regime.- 3.2 Renormalization Group Approach.- 3.3 Current-Carrying Edge States.- 3.4 Transport in Edge Channels and Other Topics.- 4. Fractional Quantum Hall Effect: Introduction.- 5. Ground State.- 5.1 Finite-Size Studies: Rectangular Geometry.- 5.2 Laughlin's Theory.- 5.3 Spherical Geometry.- 5.4 Monte Carlo Results.- 5.5 Reversed Spins in the Ground State.- 5.6 Finite Thickness Correction.- 5.7 Liquid-Solid Transition.- 5.8 Magnetoluminescence.- 6. Elementary Excitations.- 6.1 Quasiholes and Quasiparticles.- 6.2 Finite-Size Studies: Rectangular Geometry.- 6.3 Spin-Reversed Quasiparticles.- 6.4 Spherical Geometry.- 6.5 Monte Carlo Results.- 6.6 Experimental Investigations of the Energy Gap.- 6.7 Fractional Statistics and the Anyons.- 6.8 The Hierarchy: Higher Order Fractions.- 6.9 Tilted-Field Effects and Reversed-Spin States.- 7. Collective Modes: Intra-Landau Level.- 7.1 Finite-Size Studies: Spherical Geometry.- 7.2 Rectangular Geometry: Translational Symmetry.- 7.3 Spin Waves.- 7.4 Single Mode Approximation: Magnetorotons.- 8. Collective Modes: Inter-Landau Level.- 8.1 Kohn's Theorem.- 8.2 Filled Landau Level.- 8.3 Fractional Filling: Single Mode Approximation.- 8.4 Fractional Filling. Finite-Size Studies.- 9. Further Topics.- 9.1 Effect of Impurities.- 9.2 Quantization Condition.- 9.3 Higher Landau Levels.- 9.4 Even Denominator Filling Fractions.- 9.5 Multiple Layer Systems.- 9.6 Nature of Long-Range Order in the Laughlin State.- 10. Open Problems and New Directions.- Appendices.- A The Landau Wave Function in the Symmetric Gauge.- B Kubo Formalism for the Hall Conductivity.- C The Hypernetted-Chain Primer.- D Repetition of the Intra-Landau-level Mode in the Inter-Landau-level Mode.- E Characteristic Scale Values.- References.