Quantum-trajectory approach to time-dependent transport in mesoscopic systems with electron-electron interactions

It is proved that many-particle Bohm trajectories can be computed from single-particle time-dependent Schr?dinger equations. From this result, a practical algorithm for the computation of transport properties of many-electron systems with exchange and Coulomb correlations is derived. As a test, two-particle Bohm trajectories in a tunneling scenario are compared to exact results with an excellent agreement. The algorithm opens the path for implementing a many-particle quantum transport (Monte Carlo) simulator, beyond the Fermi liquid paradigm.     

Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice

In combination with Laughlin's treatment of the quantized Hall conductivity, the Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number on a periodic lattice in arbitrary dimensions. Regardless of dimensionality, interaction strength, and particle statistics (Bose or Fermi), a finite excitation gap is possible only when the particle number per unit cell of the ground state is an integer.     

A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics

We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence.     

Decoherence in a system of many two-level atoms

I show that the decoherence in a system of degenerate two-level atoms interacting with a bosonic heat bath is for any number of atoms governed by a generalized Hamming distance (called "decoherence metric") between the superposed quantum states, with a time-dependent metric tensor that is specific for the heat bath. The decoherence metric allows for the complete characterization of the decoherence of all possible superpositions of many-particle states, and can be applied to minimize the overall decoherence in a quantum memory. For qubits which are far apart, the decoherence is given by a function describing single-qubit decoherence times the standard Hamming distance. I apply the theory to cold atoms in an optical lattice interacting with blackbody radiation.     

激发态过程的多体理论方法

描述多电子体系的绝大部分参量可实验测量,如吸收光谱、发光光谱和激子效应等,都涉及电子激发态的正确描述。密度泛函理论(DFT)框架内的局域密度近似(LDA)作为第一性原理基态理论,即基于Kohn-Sham方程的解,是研究多粒子体系基态性质非常有力的工具。然而,体系激发态的第一性原理理论及其计算要比基态的理论计算复杂得多。关键问题在于描写基态和激发态时,粒子间的交换关联相互作用并不相同,而对于非均匀相互作用多粒子体系的交换关联能至今仍不清楚。不过,近年来关于激发态问题的研究,先后发展了许多描述电子激发态的理论,最重要的是基于准粒子概念和Green函数方程的多体微扰理论和含时间密度泛函理论(TDDFT)以及与此相关的描述电子-空穴相互作用的Bethe-Salpeter方程在凝聚态物理问题中的应用。其中最关键的物理量是粒子的自能算符Σ,它描述Hartree近似之外的交换和关联效应。虽然这些理论不可避免地也要引入某些近似,如对于Σ的一个好的近似就是Hedin的GW近似方法。对许多实际凝聚态体系的计算机模拟结果表明,GW近似是描述激发态问题相当成功的理论方法。将Hartree-Fock(HF)理论与LDA相结合,但采用非局域屏蔽交换代替HF方法中的局域非屏蔽交换相互作用,建立广义的KS方程(GKS),得到所谓屏蔽交换局域密度近似(sX-LDA)方法。我们在平面波自洽场方法PWscf程序包的基础上,发展了PW scf-sX-LDA方法,也是处理激发态问题及材料设计的有效方法。将评述激发态过程多体理论各种方法的发展和意义,讨论这些多体理论方法之间的联系和差异,并在此基础上介绍它们在解决半导体带带跃迁(或带隙偏小问题)、半导体及其微结构中的激子效应等重要领域的应用和成果。     

Kinetic Approach to Reaction and Diffusion in Many-Particle Systems

A derivation of hydrodynamic equations which describe diffusion in connection with reaction processes in many-particle systems is given on the basis of quantum kinetic theory. For this purpose kinetic equations are derived for a quantum gas with chemical reactions. Following Grad's method in a linear approximation reaction-diffusion equations can be obtained with explicite expressions for the diffusion and reaction rate coefficients. The influence of nonideality effects in reaction-diffusion equations is discussed.     

The emergence of classical properties through interaction with the environment

The dependence of macroscopic systems upon their environment is studied under the assumption that quantum theory is universally valid. In particular scattering of photons and molecules turns out to be essential even in intergalactic space in restricting the observable properties by locally destroying the corresponding phase relations. The remaining coherence determines the classical properties of the macroscopic systems. In this way local classical properties have their origin in the nonlocal character of quantum states.The effect of the interaction depends essentially on whether it permanently measures discrete or continuous quantities. For discrete variables (here exemplified by two-state systems) the classical properties are given by the measurement basis. The continuous case, studied for translational degrees of freedom, leads to a competition between destruction of coherence by the interaction and dispersion of the wave packet by the internal dynamics. A non-phenomenological Boltzmann-type master equation is derived for the density matrix of the center of mass. Its solutions show that the much-discussed dispersion hardly ever shows up even for small dust particles or large molecules. Instead the coherence length decreases towards the thermal de Broglie wave length of the object, whereas the incoherent spread increases. The Ehrenfest theorems are shown nevertheless to remain valid for recoil-free interactions. Some consequences of these investigations for the quantum theory of measurement are pointed out.     

Accuracy of the Time-Dependent Hartree–Fock Approximation for Uncorrelated Initial States

This article concerns the time-dependent Hartree–Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find that the TDHF approximation is accurate when there are sufficiently many particles and the initial many-particle state is any Gibbs equilibrium state for noninteracting fermions (with Slater determinants as a special example). Assuming a bounded two-particle interaction, we obtain a bound on the error of the TDHF approximation, valid for short times. We further show that the error of the TDHF approximation vanishes at all times in the mean field limit.     

Bound and Scattering States of Extended Calogero Model with an Additional PT Invariant Interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameters differ from each other in the presence of PT invariant interaction.     

An intrinsic limit to quantum coherence due to spontaneous symmetry breaking

We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry broken macroscopic systems in equilibrium. It is shown that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum coherent. This universal time scale is t(spon) approximately = 2piNH/(kBT), given in terms of the number of microscopic degrees of freedom N, temperature T, and the constants of Planck (h) and Boltzmann (kB).     

Dynamic localization in quantum dots: analytical theory

We analyze the response of a complex quantum-mechanical system (e.g., a quantum dot) to a time-dependent perturbation phi(t). Assuming the dot to be described by random-matrix theory for the Gaussian orthogonal ensemble, we find the quantum correction to the energy absorption rate as a function of the dephasing time t(phi). If phi(t) is a sum of d harmonics with incommensurate frequencies, the correction behaves similarly to that for the conductivity deltasigma(d)(t(phi)) in the d-dimensional Anderson model of the orthogonal symmetry class. For a generic periodic perturbation, the leading quantum correction is absent as in the systems of the unitary symmetry class, unless phi(-t+tau)=phi(t+tau) for some tau, which falls into the quasi-1D orthogonal universality class.     

Quantum kinetic equation for nonequilibrium dense systems

Using the density matrix method in the form developed by Zubarev, equations of motion for nonequilibrium quantum systems with continuous short range interactions are derived which describe kinetic and hydrodynamic processes in a consistent way. The T-matrix as well as the two-particle density matrix determining the nonequilibrium collision integral are obtained in the ladder approximation including the Hartree-Fock corrections and the Pauli blocking for intermediate states. It is shown that in this approximation the total energy is conserved. The developed approach to the kinetic theory of dense quantum systems is able to reproduce the virial corrections consistent with the generalized Beth-Uhlenbeck approximation in equilibrium. The contribution of many-particle correlations to the drift term in the quantum kinetic equation for dense systems is discussed.     

Two interacting spins in external fields and application to quantum computation

We study the four-level-system given by two quantum dots immersed in a time-dependent magnetic field, which are coupled to each other by an effective Heisenberg-type interaction. We describe the construction of the corresponding evolution operator in a special case of different time-dependent parallel external magnetic fields. We find a relation between the external field and the effective interaction function. The obtained results are used to analyze the theoretical implementation of a universal quantum gate.     

Wave-particle dualism and the interpretation of quantum mechanics

The realist interpretations of quantum theory, proposed by de Broglie and by Bohm, are re-examined and their differences, especially concerning many-particle systems and the relativistic regime, are explored. The impact of the recently proposed experiments of Vigier et al. and of Ghose et al. on the debate about the interpretation of quantum mechanics is discussed. An indication of how de Broglie and Bohm would account for these experimental results is given.     

Exact statements about many-particle systems with higher symmetries

A new method of calculating the energy spectrum of a system of A identical Fermi particles with translationally invariant interaction is developed under the assumption that there exists a high symmetry in the 3A-dimensional space of particle coordinates. For a special class of symmetries the many-body problem is split exactly into two sets of equations: one containing only totally symmetric combinations of the particle coordinates which are called “collective variables” and the other equation taking essentially into account the requirements of the Pauli principle and connected symmetry properties. In several cases it is possible to obtain the excitation spectra exactly showing qualitatively new features. They depend on “many-particle quantum numbers” varying independently of each other in an interval which sometimes depends on A. For special high symmetries the collective variables obey equations which are very similar to one-particle equations providing a new explanation of the “Independent-Particle Model” for arbitrary strength and form of the interaction potential. A manifold of unknown up to now excitation spectra of many-particle systems is obtained and discussed.