Showing papers on "Quantum published in 1994"
TL;DR: In this paper, King-Smith and Vanderbilt developed a complete theory in which the polarization difference between any two crystal states in a null electric field takes the form of a geometric quantum phase.
Abstract: The macroscopic electric polarization of a crystal is often defined as the dipole of a unit cell. In fact, such a dipole moment is ill defined, and the above definition is incorrect. Looking more closely, the quantity generally measured is differential polarization, defined with respect to a "reference state" of the same material. Such differential polarizations include either derivatives of the polarization (dielectric permittivity, Born effective charges, piezoelectricity, pyroelectricity) or finite differences (ferroelectricity). On the theoretical side, the differential concept is basic as well. Owing to continuity, a polarization difference is equivalent to a macroscopic current, which is directly accessible to the theory as a bulk property. Polarization is a quantum phenomenon and cannot be treated with a classical model, particularly whenever delocalized valence electrons are present in the dielectric. In a quantum picture, the current is basically a property of the phase of the wave functions, as opposed to the charge, which is a property of their modulus. An elegant and complete theory has recently been developed by King-Smith and Vanderbilt, in which the polarization difference between any two crystal states---in a null electric field---takes the form of a geometric quantum phase. The author gives a comprehensive account of this theory, which is relevant for dealing with transverse-optic phonons, piezoelectricity, and ferroelectricity. Its relation to the established concepts of linear-response theory is also discussed. Within the geometric phase approach, the relevant polarization difference occurs as the circuit integral of a Berry connection (or "vector potential"), while the corresponding curvature (or "magnetic field") provides the macroscopic linear response.
1,867 citations
TL;DR: In this article, the authors apply the surface-hopping method to proton transfer in solution, where the quantum particle is an atom, using full classical mechanical molecular dynamics for the heavy atom degrees of freedom, including the solvent molecules.
Abstract: We apply ‘‘molecular dynamics with quantum transitions’’ (MDQT), a surface‐hopping method previously used only for electronic transitions, to proton transfer in solution, where the quantum particle is an atom. We use full classical mechanical molecular dynamics for the heavy atom degrees of freedom, including the solvent molecules, and treat the hydrogen motion quantum mechanically. We identify new obstacles that arise in this application of MDQT and present methods for overcoming them. We implement these new methods to demonstrate that application of MDQT to proton transfer in solution is computationally feasible and appears capable of accurately incorporating quantum mechanical phenomena such as tunneling and isotope effects. As an initial application of the method, we employ a model used previously by Azzouz and Borgis to represent the proton transfer reaction AH–B■A−–H+B in liquid methyl chloride, where the AH–B complex corresponds to a typical phenol–amine complex. We have chosen this model, in part, because it exhibits both adiabatic and diabatic behavior, thereby offering a stringent test of the theory. MDQT proves capable of treating both limits, as well as the intermediate regime. Up to four quantum states were included in this simulation, and the method can easily be extended to include additional excited states, so it can be applied to a wide range of processes, such as photoassisted tunneling. In addition, this method is not perturbative, so trajectories can be continued after the barrier is crossed to follow the subsequent dynamics.
1,150 citations
TL;DR: The full three-dimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner–Boltzmann equation.
Abstract: The classical hydrodynamic equations can be extended to include quantum effects by incorporating the first quantum corrections These quantum corrections are $O( {\hbar ^2 } )$ The full three-dimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner–Boltzmann equation The QHD conservation laws have the same form as the classical hydrodynamic equations, but the energy density and stress tensor have additional quantum terms These quantum terms allow particles to tunnel through potential barriers and to build up in potential wellsThe three-dimensional QHD transport equations are mathematically classified as having two Schrodinger modes, two hyperbolic modes, and one parabolic mode The one-dimensional steady-state QHD equations are discretized in conservation form using the second upwind methodSimulations of a resonant tunneling diode are presented that show charge buildup in the quantum well and negative differential resistance (NDR) in the current-v
540 citations
TL;DR: It is argued that the leading quantum corrections, in powers of the energy or inverse power of the distance, may be computed in quantum gravity through knowledge of only the low-energy structure of the theory.
Abstract: I argue that the leading quantum corrections, in powers of the energy or inverse powers of the distance, may be computed in quantum gravity through knowledge of only the low-energy structure of the theory. As an example, I calculate the leading quantum corrections to the Newtonian gravitational potential.
537 citations
TL;DR: In this paper, a recursive application of the elementary mapping step, termed the propagator, is presented, in a time-dependent description of quantum molecular dynamics, where a propagator U(z) maps the waw-function at time t, p(t) to the wave function at time n + n, 0(t+n) = n 0(n)0(t).
Abstract: INTROIDUCTION Our current understanding of molecular dynamics uses quantum mechanics as the basic underlying theory to elucidate thc processes involved. Establishing numerical schemes to solve the quantum equations of motion is crucial for understanding realistic molecular encounters. The introduction of pseudo-spectral methods has been an important step in this direction. These methods allow an extremely accurate representation of the action of an operator, usually the Hamiltonian, on a wavefunction: q~ = fI~p. A solution for the quantum molecular dynamics can be obtained by recursively applying the elementary mapping step. This recursive application of the elementary step, termed the propagator, is the subject of this review. The na~:ural application of a propagator is in a time-dependent description of quantum molecular dynamics, where the propagator U(z) maps the waw~function at time t, ~p(t) to the wavefunction at time t + ~: 0(t+ ~) = ~(z)0(t). The decomposition into a recursive application of the elementary step is performed by a polynomial expansion of the propagator. The introduction of the Chebychev polynomial expansion (l) first created a propagation scheme that could match the accuracy of the
516 citations
TL;DR: In this paper, the capacity of a communication channel is the maximum rate at which information can be transmitted without error from the channel's input to its output, i.e., the time it takes to decode the information from the input to the output.
Abstract: The capacity C of a communication channel is the maximum rate at which information can be transmitted without error from the channel's input to its output. The authors review quantum limits on the capacity that can be achieved with linear bosonic communication channels that have input power P. The limits arise ultimately from the Einstein relation that a field quantum at frequency f has energy E=hf. A single linear bosonic channel corresponds to a single transverse mode of the bosonic field i.e., to a particular spatial dependence in the plane orthogonal to the propagation direction and to a particular spin state or polarization. For a single channel the maximum communication rate is CWB=( ln 2)2P3h bits/s. This maximum rate can be achieved by a "number-state channel," in which information is encoded in the number of quanta in the bosonic field and in which this information is recovered at the output by counting quanta. Derivations of the optimum capacity CWB are reviewed. Until quite recently all derivations assumed, explicitly or implicitly, a number-state channel. They thus left open the possibility that other techniques for encoding information on the bosonic field, together with other ways of detecting the field at the output, might lead to a greater communication rate. The authors present their own general derivation of the single-channel capacity upper bound, which applies to any physically realizable technique for encoding information on the bosonic field and to any physically realizable detection scheme at the output. They also review the capacities of coherent communication channels that encode information in coherent states and in quadrature-squeezed states. A three-dimensional bosonic channel can employ many transverse modes as parallel single channels. An upper bound on the information flux that can be transferred down parallel bosonic channels is derived.
378 citations
TL;DR: In this paper, it was shown that if the classical time correlation functions are rescaled to account for the ratio of quantum to classical fluctuations, providing a quantum mechanical treatment for the solute and the solvent, the relaxation rates and the entire absorption spectrum are the same as for a purely classical treatment.
Abstract: The time correlation function for a harmonic quantum mechanical system can be related to the time correlation function for a corresponding classical system. Although straightforward to derive and well known in other contexts, this relationship has been unappreciated in the context of vibrational relaxation, where time correlation functions obtained from classical molecular dynamics have been used to predict relaxation rates for a quantum solute in a classical solvent. This inconsistent treatment—quantum solute, classical solvent—predicts a relaxation rate which is slower than if the entire system, both solute and solvent, were treated classically. We demonstrate that if the classical time correlation functions are rescaled to account for the ratio of quantum to classical fluctuations, providing a quantum mechanical treatment for the solute and the solvent, the relaxation rates and the entire absorption spectrum are the same as for a purely classical treatment. Our conclusions are valid when the solute and...
339 citations
TL;DR: In this article, the authors consider the problem of relating the timelessness of the quantum field theory with the evidence of the flow of time, and propose a unified perspective on these problems, based on the hypothesis that in a generally covariant quantum theory the physical time flow is not a universal property of the mechanical theory, but rather it is determined by the thermodynamical state of the system (thermal time hypothesis).
Abstract: We consider the cluster of problems raised by the relation between the notion of time, gravitational theory, quantum theory and thermodynamics; in particular, we address the problem of relating the `timelessness' of the hypothetical, fundamental generally covariant quantum field theory with the `evidence' of the flow of time. By using the algebraic formulation of quantum theory, we propose a unifying perspective on these problems, based on the hypothesis that in a generally covariant quantum theory the physical time flow is not a universal property of the mechanical theory, but rather it is determined by the thermodynamical state of the system (`thermal time hypothesis'). We implement this hypothesis by using a key structural property of von Neumann algebras: the Tomita--Takesaki theorem, which allows us to derive a time flow, namely a one-parameter group of automorphisms of the observable algebra, from a generic thermal physical state. We study this time flow, its classical limit, and we relate it to various characteristic theoretical facts, such as the Unruh temperature and the Hawking radiation. We point out the existence of a state-independent notion of `time', given by the canonical one-parameter subgroup of outer automorphisms provided by the co-cycle Radon--Nikodym theorem.
324 citations
TL;DR: The squeezed state formalism provides an interesting framework within which to study the amplification process, but it is concluded that it does not provide us with any new physical results.
Abstract: Inflationary cosmology is analyzed from the point of view of squeezed quantum states. As noted by Grishchuk and Sidorov, the amplification of quantum fluctuations into macroscopic perturbations which occurs during cosmic inflation is a process of quantum squeezing. We carefully develop the squeezed state formalism and derive the equations that govern the evolution of a Gaussian initial state. We derive the power spectrum of density perturbations for a simple inflationary model and discuss its features. We conclude that the squeezed state formalism provides an interesting framework within which to study the amplificaiton process, but, in disagreement with the claims of Grishchuk and Sidorov, that it does not provide us with any new physical results.
307 citations
TL;DR: The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schrodinger equation in which the wave function is the probability distribution and the Hamiltonian is that of a quantum chain with nearest neighbor interactions as discussed by the authors.
TL;DR: A real-time approach is developed that allows the diagrammatic classification of resonant tunneling processes where different electrons tunnel coherently back and forth between the leads and the metallic island.
Abstract: Coulomb-blockade phenomena and quantum fluctuations are studied in mesoscopic metallic tunnel junctions with high charging energies. If the resistance of the barriers is large compared to the quantum resistance, transport can be described by sequential tunneling. Here we study the influence of quantum fluctuations. They are strong when the resistance is small or the temperature is very low. A real-time approach is developed that allows the diagrammatic classification of resonant tunneling processes where different electrons tunnel coherently back and forth between the leads and the metallic island. With the help of a nonperturbative resummation technique we evaluate the spectral density, which describes the charge excitations of the system. From it, physical quantities of interest such as current and average charge can be deduced. Our main conclusions are as follows: An energy renormalization leads to a logarithmic temperature dependence of the renormalized system parameters. A finite lifetime broadening can change the classical picture drastically. It gives rise to a strong flattening of the Coulomb oscillations for low resistances, but in the Coulomb-blockade regime inelastic electron cotunneling persists. The effects become important at temperatures that are accessible in experiments.
TL;DR: In this paper, the authors used the quasiadiabatic propagator path integral (QUAPI) methodology to evaluate the flux-flux correlation function whose time integral determines the rate coefficient.
Abstract: We present accurate fully quantum calculations of thermal rate constants for a symmetric double well system coupled to a dissipative bath. The calculations are performed using the quasiadiabatic propagator path integral (QUAPI) methodology to evaluate the flux–flux correlation function whose time integral determines the rate coefficient. The discretized path integral converges very rapidly in the QUAPI representation, allowing efficient calculation of quantum correlation functions for sufficiently long times. No ad hoc assumption is introduced and thus these calculations yield the true quantum mechanical rate constants. The results presented in the paper demonstrate the applicability of the QUAPI methodology to practically all regimes of chemical interest, from thermal activation to deep tunneling, and the quantum transmission factor exhibits a Kramers turnover. Our calculations reveal an unusual step structure of the integrated reactive flux in the weak friction regime as well as quantum dynamical enhancement of the rate above the quantum transition state theory value at low temperatures, which is largely due to vibrational coherence effects. The quantum rates are compared to those obtained from classical trajectory simulations. We also use the numerically exact classical and quantum results to establish the degree of accuracy of several analytic and numerical approximations, including classical and quantum Grote–Hynes theories, semiclassical transition state theory (periodic orbit) estimates, classical and quantum turnover theories, and the centroid density approximation.
TL;DR: A generalized expression is developed for the DQE of a cascaded imaging system that is dependent only on the gain, gain Poisson excess (related to the variance), and MTF, of each stage, and a direct relationship is shown to exist between the D QE and values in the QAD.
Abstract: The detective quantum efficiency (DQE) is a system parameter that can be used to accurately describe image noise transfer characteristics through many imaging systems. A simpler approach used by some investigators, particularly when evaluating new ideas and system designs, is to describe the system as a series of cascaded stages. Each stage may correspond to either an increase in the number of quanta (e.g., conversion from x-ray to optical quanta in a radiographic screen), or a loss (a detection or coupling probability). The number of secondary quanta at each stage per incident primary quantum is given by the product of all preceding gains, and can be displayed graphically for convenient interpretation. The stage with the fewest quanta is called the "quantum sink," limiting the pixel signal-to-noise ratio to less than the square root of the number of quanta per pixel. This conventional zero-spatial-frequency "quantum accounting diagram" (QAD), however, neglects the spatial spreading of secondary quanta and can seriously underestimate image noise. It is shown that this problem is avoided with the introduction of a spatial-frequency dependent QAD, expressed as the product of the gains and squared modulation-transfer functions (MTF) of each stage. A generalized expression is developed for the DQE of a cascaded imaging system that is dependent only on the gain, gain Poisson excess (related to the variance), and MTF, of each stage. A direct relationship is then shown to exist between the DQE and values in the QAD. The QAD of a hypothetical system consisting of a charge-coupled device camera and a scintillating screen is evaluated as an illustrative example. The conventional zero-frequency analysis suggests two quantum sinks occur with approximately equal importance: one in the number of x rays, and one in the number of optical quanta. The spatial-frequency dependent analysis, however, shows the optical quantum sink becomes severe and dominates at nonzero frequencies. The necessary increase in gain or optical numerical aperture required to prevent the optical quantum sink for spatial frequencies of interest is determined from the QAD analysis. The visual impact of this nonzero spatial-frequency quantum sink is shown in images generated using a Monte Carlo simulation of the cascading process.
TL;DR: In this article, the conductance of a ballistic quantum dot (with chaotic classical dynamics and being coupled by ballistic point contacts to two electron reservoirs) is computed on the single assumption that its scattering matrix is a member of Dyson's circular ensemble.
Abstract: The conductance of a ballistic quantum dot (having chaotic classical dynamics and being coupled by ballistic point contacts to two electron reservoirs) is computed on the single assumption that its scattering matrix is a member of Dyson's circular ensemble. General formulae are obtained for the mean and variance of transport properties in the orthogonal (β = 1), unitary (β = 2), and symplectic (β = 4) symmetry class. Applications include universal conductance fluctuations, weak localization, sub-Poissonian shot noise, and normal-metal-superconductor junctions. The complete distribution P(g) of the conductance g is computed for the case that the coupling to the reservoirs occurs via two quantum point contacts with a single transmitted channel. The result P(g) ∝ g−1 + β/2 is qualitatively different in the three symmetry classes.
TL;DR: In this paper, Lanczos diagonalizatioin technique and random sampling is used to evaluate finite-temperature static and dynamical quantities in small many-body quantum systems, such as the optical conductivity of a single charge-carrier hole in the system of strongly correlated electrons.
Abstract: A method, using the Lanczos diagonalizatioin technique and random sampling, is introduced to evaluate finite-temperature static and dynamical quantities in small many-body quantum systems. As an example the method is applied to the calculation of the optical conductivity of a single charge-carrier hole in the system of strongly correlated electrons, as described by the t-J model.
01 Dec 1994
TL;DR: In this article, an elliptic quantum group associated with each simple classical Lie algebra is constructed, which is closely related to elliptic face models of statistical mechanics, and, in its semiclassical limit, to the Wess-Zumino-Witten model of conformal field theory on tori.
Abstract: This note for the Proceedings of the International Congress of Mathematical Physics gives an account of a construction of an ``elliptic quantum group'' associated with each simple classical Lie algebra. It is closely related to elliptic face models of statistical mechanics, and, in its semiclassical limit, to the Wess-Zumino-Witten model of conformal field theory on tori.
TL;DR: In this paper, the authors discuss and give evidence for the existence of a new mechanism for quantum dynamical tunneling, which may occur when a quantum system's underlying classical dynamics are far from integrability.
Abstract: We discuss and give evidence for the existence of a new mechanism for quantum dynamical tunneling. It may occur when a quantum system's underlying classical dynamics are far from integrability. In these circumstances, we show that the dominant tunneling contributions arise through chaos-assisted processes. This leads to behavior that is drastically different from that found in integrable and quasi-integrable systems. In particular, one can observe a marked crossing mechanism when a chaotic level passes nearby the tunneling ones, and the distributions of splitting (due to tunneling) can be modeled using properly designed ensembles of random matrices. Such tunneling should be amenable to experimental detection.
TL;DR: Using energy correlated photon pairs created in parametric down-conversion, the authors demonstrate two-photon interference effects in fiber interferometers separated by 4.3 km of optical fiber.
Abstract: Using energy correlated photon pairs created in parametric down-conversion we demonstrate two-photon interference effects in fiber interferometers separated by 4.3 km of optical fiber. The measured 86% interference visibilities confirm the purely quantum mechanical origin of these correlations.
TL;DR: In this paper, the authors describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly.
Abstract: Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *-operation and a positive inner product.
TL;DR: This work extends the derivation of Niu and Thouless for quantized charge transport to the case where the quantum adiabatic evolution is noncyclic, and shows how this polarization difference can be written in terms of a Berrys phase for a system with many-body interactions.
Abstract: During past decades, concepts about the electrostatics of infinite systems have been a challenge for theoretical physicists. In particular, the question of whether the absolute macroscopic polarization or the difference between the polarizations of two states of an insulating crystal is a well-defined bulk property has remained a controversial one. Recently, King-Smith and Vanderbilt, and Resta have provided an approach in terms of the geometric Berrys phase of electronic orbitals in an independent-particle approximation. Here we extend the derivation of Niu and Thouless for quantized charge transport to the case where the quantum adiabatic evolution is noncyclic, and we show how this polarization difference can be written in terms of a Berrys phase for a system with many-body interactions. We also discuss the origin and magnitude of the ``quantum uncertainty'' that appears when a path-independent gauge is used to compute those geometric quantum phases. This geometric viewpoint not only helps us understand the issues raised above but provides a mathematical method to compute polarizations in a many-body framework.
TL;DR: By taking into account both quantum mechanical and general relativistic effects, an equation that describes some limitations on the measurability of space-time distances can be derived as mentioned in this paper, and possible features of quantum gravity which are suggested by this equation.
Abstract: By taking into account both quantum mechanical and general relativistic effects, an equation that describes some limitations on the measurability of space-time distances can be derived. We then discuss possible features of quantum gravity which are suggested by this equation.
TL;DR: In this article, the authors summarize recent theoretical and experimental studies of helium and molecular hydrogen clusters, focusing primarily on techniques developed to address the quantum nature of these systems, as well as indicators of superfluid behaviour.
Abstract: Quantum clusters are van der Waals aggregates of light atomic and molecular species whose behaviour is dominated by quantum delocalization and exchange effects. We summarize here recent theoretical and experimental studies of helium and molecular hydrogen clusters, focusing primarily on techniques developed to address the quantum nature of these systems. Indicators of superfluid behaviour are discussed, as well as the use of molecular probe species to study structural and dynamical properties.
TL;DR: In this article, the role of renormalization effects in photoexcited semiconductors is discussed, in particular the role in the fading of the electron-phonon interaction.
Abstract: The carrier dynamics in photoexcited semiconductors is studied in a quantum kinetic approach based on the density-matrix formalism. Besides the memory effects related to the energy-time uncertainty, we discuss interference effects between different types of interactions describing the fact that a transition due to one interaction occurs between states, which are renormalized by other interactions. We first analyze the relaxation process in a one-band model, which allows us to concentrate on memory effects in the electron-phonon interaction. We then extend the model to a two-band semiconductor interacting with a short laser pulse, which is more realistic due to the explicit treatment of the carrier generation process. Here we discuss, in particular, the role of renormalization effects. It turns out that these effects reduce the broadening due to the non-Markovian dynamics and lead to distribution functions, which are more similar to the semiclassical case; the positions of the peaks, however, exhibit slight time-dependent shifts. On the other hand, phonon quantum beats in the decay of the interband polarization are increased by these renormalization effects.
01 Jan 1994
TL;DR: In this article, it is argued that the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time.
Abstract: The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why so-far no completely consistent mathematical models of quantum black holes have been found.
Essay dedicated to Abdus Salam.
TL;DR: It is shown that quantum finite-size effects can be taken into account by a simple semiclassical correction to the Sharvin formula and that the conductance of a circular point contact deviates from the classical Sharvin result.
Abstract: An exact calculation of the quantum conduction through a curvilinear constriction in a three-dimensional electron gas is presented. We show that the conductance behavior presents significant differences with respect to the two-dimensional case. Importantly, we find that the conductance of a circular point contact deviates from the classical Sharvin result and the conductance per unit area is not constant except in the limit of macroscopic areas. We show that quantum finite-size effects can be taken into account by a simple semiclassical correction to the Sharvin formula. Recent experiments and calculations on quantum constrictions formed in atomic-scale point contacts are discussed.
TL;DR: In this paper, the authors analyse and develop the recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalised quantum theory based on the ideas of histories and decoherence functionals.
Abstract: We analyse and develop the recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalised form of quantum theory based on the ideas of histories and decoherence functionals. Particular stress is placed on properties of the space of decoherence functionals, including one way in which certain global and topological properties of a classical system are reflected in a quantum history theory.
TL;DR: In this article, the quantum transmission properties of serial stub and loop structures are studied and compared with the conventional periodic-potential scatterers, and essential differences are pointed out.
Abstract: We have studied the quantum transmission properties of serial stub and loop structures. Throughout we have considered free-electron networks and the scattering arises solely due to the geometric nature of the problem. The band formation in these geometric structures is analyzed and compared with the conventional periodic-potential scatterers. Some essential differences are pointed out. We show that a single defect in an otherwise periodic structure modifies band properties nontrivially. By a proper choice of a single defect one can produce positive-energy bound states in continuum, in the sense of von Neumann and Wigner. We also discuss some magnetic properties of loop structures in the presence of Aharonov-Bohm flux.
TL;DR: In this paper, it was shown that two-body operators acting on a Fock space with either fermionic or no statistics are bounded below by one-body operator which mimic exchange effects.
Abstract: We consider some two-body operators acting on a Fock space with either fermionic or no statistics. We prove that they are bounded below by one-body operators which mimic exchange effects. This allows us to compare two-body correlations of fermionic and bosonic systems with those in Hartree-Fock, respectively Hartree theory. Applications of the fermionic estimate yield lower bounds for the ground state energy of jellium at high densities and of molecules with large nuclear charges.