Low-energy spectrum and finite temperature properties of quantum rings

Recently it was demonstrated that the rotational and vibrational spectra of quantum rings containing few electrons can be described quantitatively by an effective spin-Hamiltonian combined with rigid center-of-mass rotation and internal vibrations of localized electrons. We use this model Hamiltonian to study the quantum rings at finite temperatures and in presence of a nonzero magnetic field. Total spin, angular momentum and pair correlation show similar phase diagram which can be understood with help of the rotational spectrum of the ring. Received 18 January 2002 Published online 13 August 2002     

The density of energy flow of quasiparticles with arbitrary energy–momentum relation

In this paper, we consider the energy conservation law in a continuous medium with arbitrary energy–momentum relation. We use a new theoretical approach in which both the long wavelength and short wavelength thermal excitations are described in a unified way. The theory is based on the fact that in a quantum fluid, the thermal de Broglie wavelengths of the atoms overlap each other. In this case, the atoms are delocalized in space and we can treat a quantum fluid as a continuous medium without any restriction on length scale. So, in quantum liquids, we can determine the probabilistic values of the parameters of the continuous medium in every mathematical point of space. From the Hamiltonian of this system, we derive a system of linear equations for the general case of an ideal liquid, which has a nonlocal relationship between pressure and density. In the frame of this model from the energy conservation law, a general expression for the energy density flow is obtained. It is shown that for the wave packet, it is not affected by the freedom in its definition. A clear relation for the energy density flow of a wave packet is derived that generalizes the ordinary form of it to the case of arbitrary dispersion.     

Thermodyamic Bounds on Drude Weights in Terms of Almost-conserved Quantities

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki’s proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain (Prosen, in Phys Rev Lett 106:217206, 2011).     

Microscopic calculation of the inclusive electron scattering structure function in 16O

We calculate the charge form factor and the longitudinal structure function for 16O and compare with the available experimental data, up to a momentum transfer of 4 fm(-1). The ground-state correlations are generated using the coupled-cluster [ exp(S)] method, together with the realistic v18 NN interaction and the Urbana IX three-nucleon interaction. Center-of-mass corrections are dealt with by adding a center-of-mass Hamiltonian to the usual internal Hamiltonian, and by means of a many-body expansion for the computation of the observables measured in the center-of-mass system.     

An effective Hamiltonian approach to quantum random walk

In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.     

共轭线性对称性及其对PT-对称量子理论的应用

传统量子系统的哈密顿是自伴算子,哈密顿的自伴性不仅保证系统遵循酉演化和保持概率守恒,而且也保证了它自身具有实的能量本征值,这类系统称为自伴量子系统.然而,确实存在一些物理系统(如PT-对称量子系统),其哈密顿不是自伴的,这类系统称为非自伴量子系统.为了深入研究PT-对称量子系统,并考虑到算子PT的共轭线性性,首先讨论了共轭线性算子的一些性质,包括它们的矩阵表示和谱结构等;其次,分别研究了具有共轭线性对称性和完整共轭线性对称性的线性算子,通过它们的矩阵表示,给出了共轭线性对称性和完整共轭线性对称性的等价刻画;作为应用,得到了关于PT-对称及完整PT-对称算子的一些有趣性质,并通过一些具体例子,说明了完整PT-对称性对张量积运算不具有封闭性,同时说明了完整PT-对称性既不是哈密顿算子在某个正定内积下自伴的充分条件,也不是必要条件.     

The Symmetries of Fermion Fluids at Low Dimensions

We point out that the quasiparticle spectrum of the Landau Fermi liquid theory has an extra Z₂ symmetry, local in momentum space, which is not generic to the Hamiltonian with interactions. Thus the Fermi liquid is in this sense a (quantum) zero-temperature critical point.     

Einstein-Podolsky-Rosen constraints on quantum action at a distance: The Sutherland paradox

Assuming that future experiments confirm Aspect's discovery of nonlocal interactions between quantum pairs of correlated particles, we analyze the constraints imposed by the EPR reasoning on the said interactions. It is then shown that the nonlocal relativistic quantum potential approach plainly satisfies the Einstein causality criteria as well as the energy-momentum conservation in individual microprocesses. Furthermore, this approach bypasses a new causal paradox for timelike separated EPR measurements deduced by Sutherland in the frame of an approach by means of space-time zigzags with advanced potentials. It is finally demonstrated that this inherent quantum causal direct interaction establishes permanent EPR correlations which are always restricted to spacelike separations and are instantaneous only in the center-of-mass rest frame of the two-particle system.     

光线量子理论研究薄膜介质光场能量分布

因为光线量子力学方程的光线哈密顿算符不表示能量,而是具有可变折射率的物理意义,因此应用光线量子论讨论波导中光场能量分布是一个有待研究的问题.本文借鉴量子力学几率密度和几率密度矢量概念推导出光场能量分布的普遍性公式,并证明流线结构的光场中守恒定律的成立.     

Exact microscopic wave function for a topological quantum membrane

The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this microscopic ground state wave function describes a topological quantum membrane. We also construct variational wave functions for excited states using the noncommutative algebra on the four sphere. Our approach introduces a nonperturbative method to quantize topological membranes.     

Vacuum structures in Hamiltonian light-front dynamics

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic nonperturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.     

Applications of Noether conservation theorem to Hamiltonian systems

The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.     

Differential conservation laws in nonrelativistic quantum mechanics

Differential conservation laws for quantum mechanical operator fields are studied from a) some general point of view and b) to find the particle, momentum and energy conservation law, if the Hamiltonian isnot local as usually assumed. Concerning (b): If the interaction in a many body system is nonlocal, the particle current operator in the continuity equation has to be redefined. Physical properties of the interaction current are discussed. Similar nonlocal effects must be taken care of in the stress and energy current operator. Concerning (a): Besides the mentioned conservation laws there are arbitrary many other ones. In fact, for each arbitrary field a class of corresponding currents exists and vice versa, which together are related by a differential conservation law. Some physical aspects for defining current operators are given and discussed.     

Manifestation of Hamiltonian chaos in dissipative atomic transport in a standing-wave laser field

We simulate atomic ballistic transport in a standing-wave laser field in the framework of a Monte Carlo stochastic wavefunction approach in which the coherent Hamiltonian evolution is interrupted at random times by spontaneous emission events. It is shown in numerical experiments and confirmed analytically that the character of spatial and momentum diffusion of spontaneously emitting atoms changes abruptly in the atom-laser detuning regime where the deterministic Hamiltonian dynamics has been shown to be chaotic. Thus, we find a manifestation of underlying Hamiltonian chaos in the diffusive-like center-of-mass motion which can be observed in real experiments. The article is published in the original.     

Fidelity in the center-of-mass tomography

The notion of the center-of-mass tomogram is introduced for describing the classical states of multipartite systems. The center-of-mass tomographic-probability representation of the quantum states is used to calculate the fidelity of multipartite quantum states in an explicit integral form.     

Measure synchronization in hybrid quantum-classical systems

Measure synchronization in hybrid quantum-classical systems is investigated in this paper. The dynamics of the classical subsystem is described by the Hamiltonian equations, while the dynamics of the quantum subsystem is governed by the Schrödinger equation. By increasing the coupling strength in between the quantum and classical subsystems, we reveal the existence of measure synchronization in coupled quantum-classical dynamics under energy conservation for the hybrid systems.     

Measurement of the Wigner Characteristic Function for the Center-of-Mass Motion of Two Trapped Ions

We proposed a scheme for the reconstruction of the quantum states for the center-of-mass vibrationalmode of two trapped ions. In the scheme the ions are multichromatically excited by three lasers. Then measurementof the difference between probabilities of the ions being both in electronic ground and excited states directly yields theWigner characteristic function for the center-of-mass vibrational state. The scheme can also be used to prepare entangledcoherent states for the center-of-mass and relative vibrational modes.     

Sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment

We find the necessary and sufficient conditions for the entropy rate of the system to be zero under any system-environment Hamiltonian interaction. We call the class of system-environment states that satisfy this condition lazy states. They are a generalization of classically correlated states defined by quantum discord, but based on projective measurements of any rank. The concept of lazy states permits the construction of a protocol for detecting global quantum correlations using only local dynamical information. We show how quantum correlations to the environment provide bounds to the entropy rate, and how to estimate dissipation rates for general non-Markovian open quantum systems.     

Measurement of the Wigner Characteristic Function for the Center－of－Mass Motion of Two Trapped Ions

We proposed a scheme for the reconstruction of the quantum states for the center-of-mass vibrational mode of two trapped ions. In the scheme the ions are multichromatically excited by three lasers. Then measurement of the difference between probabilities of the ions being both in electronic ground and excited states directly yields the Wigner characteristic function for the center-of-mass vibrational state. The scheme can also be used to prepare entangled coherent states for the center-of-mass and relative vibrational modes.