Classical and quantum pumping in closed systems

Pumping of charge (Q) in a closed ring geometry is not quantized even in the strict adiabatic limit. The deviation form exact quantization can be related to the Thouless conductance. We use the Kubo formalism as a starting point for the calculation of both the dissipative and the adiabatic contributions to Q. As an application we bring examples for classical dissipative pumping, classical adiabatic pumping, and in particular we make an explicit calculation for quantum pumping in case of the simplest pumping device, which is a three site lattice model. We make a connection with the popular S-matrix formalism which has been used to calculate pumping in open systems.     

Hamiltonian quantum dynamics with separability constraints

Schroedinger equation on a Hilbert space H, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space PH. Separable states of a bipartite quantum system form a special submanifold of PH. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example the system of two interacting qubits. The constraints introduce nonlinearities which render the dynamics nontrivial. We show that the qualitative properties of the constrained dynamics clearly manifest the symmetry of the qubits system. In particular, if the quantum Hamilton’s operator has not enough symmetry, the constrained dynamics is nonintegrable, and displays the typical features of a Hamiltonian dynamical system with mixed phase space. Possible physical realizations of the separability constraints are discussed.     

Divergence-free WKB theory

We present a divergence-free WKB theory, which is a new semiclassical theory modified by nonperturbative quantum corrections. Conventionally, the WKB theory is constructed upon a trajectory that obeys the bare classical dynamics expressed by a quadratic equation in momentum space. Contrary to this, the divergence-free WKB theory is based on a higher-order algebraic equation in momentum space, which represents a dressed classical dynamics. More precisely, this higher-order algebraic equation is obtained by including quantum corrections to the quadratic equation, which is the bare classical limit. An additional solution of the higher-order algebraic equation enables us to construct a uniformly converging perturbative expansion of the wavefunction. Namely, our theory removes the notorious divergence of wavefunction at a turning point from the WKB theory. Moreover, our theory is able to produce wavefunctions and eigenenergies more accurate than those given by the traditional WKB method. In addition, the divergence-free WKB theory that is based on the cubic equation allows us to construct a uniformly valid wavefunction for the nonlinear Schrödinger equation (NLSE). A recent short letter [T. Hyouguchi, S. Adachi, M. Ueda, Phys. Rev. Lett. 88 (2002) 170404] is the opening of the divergence-free WKB theory. This paper presents full formalism of this theory and its several applications concerning wavefunction and eigenenergy to show that our theory is a natural extension of the traditional WKB theory that incorporates nonperturbative quantum corrections.     

Multidimensional quantum dynamics and infrared spectroscopy of hydrogen bonds

Hydrogen bonds are of outstanding importance for many processes in Chemistry, Biology, and Physics. From the theoretical perspective the small mass of the proton in a hydrogen bond makes it the primary quantum nucleus and the phenomena one expects to surface in a particular clear way are, for instance, zero-point energy effects, quantum tunneling, or coherent wave packet dynamics. While this is well established in the limit of one-dimensional motion, the details of the multidimensional aspects of the dynamics of hydrogen bonds are just becoming accessible to experiments and numerical simulations.     

? expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

We extend a theory of first order ? corrections to Gutzwiller’s trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C_4v-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the ? expansion method.     

Semiclassical theory of transport in antidot lattices

Motivated by a recent experiment by Weiss et al. [Phys. Rev. Lett. 70, 4118 (1993)], we present a detailed study of quantum transport in large antidot arrays whose classical dynamics is chaotic. We calculate the longitudinal and Hall conductivities semiclassically starting from the Kubo formula. The leading contribution reproduces the classical conductivity. In addition, we find oscillatory quantum corrections to the classical conductivity which are given in terms of the periodic orbits of the system. These periodic-orbit contributions provide a consistent explanation of the quantum oscillations in the magnetoconductivity observed by Weiss et al. We find that the phase of the oscillations with Fermi energy and magnetic field is given by the classical action of the periodic orbit. The amplitude is determined by the stability and the velocity correlations of the orbit. The amplitude also decreases exponentially with temperature on the scale of the inverse orbit traversal time/T . The Zeeman splitting leads to beating of the amplitude with magnetic field. We also present an analogous semiclassical derivation of Shubnikov-de Haas oscillations where the corresponding classical motion is integrable. We show that the quantum oscillations in antidot lattices and the Shubnikov-de Haas oscillations are closely related. Observation of both effects requires that the elastic and inelastic scattering lengths be larger than the lengths of the relevant periodic orbits. The amplitude of the quantum oscillations in antidot lattices is of a higher power in Planck's constant and hence smaller than that of Shubnikov-de Haas oscillations. In this sense, the quantum oscillations in the conductivity are a sensitive probe of chaos.This paper is dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

Linear transformations of quantum states

This paper considers the most general linear transformation of a quantum state. We enumerate the conditions necessary to retain a physical interpretation of the transformed state: hermiticity, normalization and complete positivity. We show that these can be formulated in terms of an associated transformation introduced by Choi in 1975. We extend his treatment and display the mathematical argumentation in a manner closer to that used in traditional quantum physics. We contend that our approach displays the implications of the physical requirements in a simple and intuitive way. In addition, defining an arbitrary vector, we may derive a probability distribution over the spectrum of the associated transformation. This fixes the average of the eigenvalue independently of the vector chosen. The formal results are illustrated by a couple of examples.     

The laser-dressed potential binding energy of a hydrogenic impurity in a spherical quantum dot by the analytical transfer matrix method

The analytical transfer matrix method (ATMM) is efficient and accurate for understanding the nature of bound states. In this paper, it is applied to obtain the binding energy of a hydrogenic impurity placed at the center of the spherical quantum dots (QDs) in an intense laser field. Our results agree with the exact energies in Varshni [Superlattices Microstructures 30 (2001) 45]. Therefore, ATMM gives us an alternative approach to tackle the problem of impurities placed in nano-structures under intense laser fields.     

Strategies to measure a quantum state

We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a “typical” probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of “best strategy” (i.e., the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all “best” strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.     

Bandt-Pompe-Tsallis quantifier and quantum-classical transition

We concern ourselves with statistical quantifiers of semiclassical time-evolutions and their classical limit. The system of interest represents the interaction between matter and a given field. Our tool here is the so-called Permutation Entropy, evaluated by recourse to the so-called Bandt-Pompe technique, within a Tsallis scenario. We encounter that the most salient details of the quantum-classical transition are well-described, indeed, in a better fashion than that of previous approaches.     

Excited state quantum phase transitions in many-body systems

Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean-field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions.     

Quantum treatment of the time-dependent coupled oscillators under the action of a random force

In this communication we introduce the problem of time-dependent frequency converter under the action of external random force. We have assumed that the coupling parameter and the phase pump are explicitly time dependent. Using the equations of motion in the Heisenberg picture the dynamical operators are obtained, however, under a certain integrability condition. When the system is initially prepared in the even coherent states the squeezing phenomenon is discussed. The correlation function is also considered and it has been shown that the nonclassical properties are apparent and sensitive to any variation in the integrability parameter. Furthermore, the wave function in Schrödinger picture is calculated and used it to derive the wave function in the coherent states. The accurate definition of the creation and annihilation operators are also introduced and employed to diagonalize the Hamiltonian system.     

Quantum effects of periodic orbits for the kicked top

We analyze traces of powers of the time evolution operator of a periodically kicked top. Semiclassically, such traces are related to periodic orbits of the classical map. We derive the semiclassical traces in a coherent state basis and show how the periodic orbits can be recovered via a Fourier transform. A breakdown of the stationary phase approximation is detected. The quasi energy spectrum remains elusive due to lack of knowledge of sufficiently many periodic orbits. Divergencies of periodic orbit formulas are avoided by appealing to the finiteness of the quantum mechanical Hilbert space. The traces also enter the coefficients of the characteristic polynominal of the Floquet operator. Statistical properties of these coefficients give rise to a new criterion for the distinction of chaos and regular motion.     

Molecular spectra, quantum chaos, and scars

Low resolution features in the spectra of classically chaotic atomic and molecular systems are known to be related to recurrences induced by classical periodic motions. In this paper we study how such characteristics reveal in the LiNC/LiCN isomerizing molecular system, and describe how the transition from regularity to classical chaos that takes place in this system shows up at quantum level in the structure of the corresponding wavefunctions in the form of “scars”. To this end we use some projection techniques, based on the propagation of wave packets, which have been developed in our laboratory. In this way some regions at the border of the chaotic region can be detected, in which the systematics of “scar” formation can be studied at a very elementary level, without complications due to the high level density which are customarily used in this type of studies in order to achieve the semiclassical limit. Received: 16 March 1998 / Revised: 23 April 1998 / Accepted: 4 May 1998     

Semiclassical limits for the QCD Dirac operator

We identify three semiclassical parameters in the QCD Dirac operator. Mutual coupling of the different types of degrees of freedom (translational, colour and spin) depends on how the semiclassical limit is taken. We discuss various semiclassical limits and their potential to describe spectrum and spectral statistics of the QCD Dirac operator close to zero virtuality.     

Simple approach to the mesoscopic open electron resonator: quantum current oscillations

The open electron resonator, described by Duncan et al. [D.S. Duncan, M.A. Topinka, R.M. Westervelt, K.D. Maranowski, A.C. Gossard, Phys. Rev. B 64 (2001) 033310. [1]], is a mesoscopic device that has attracted considerable attention due to its remarkable behaviour (conductance oscillations), which has been explained by detailed theories based on the behaviour of electrons at the top of the Fermi sea. In this work, we study the resonator using the simple quantum quantum electrical circuit approach, developed recently by Li and Chen [Y.Q. Li, B. Chen, Phys. Rev. B 53 (1996) 4027. [2]]. With this approach, and considering a very simple capacitor-like model of the system, we are able to theoretically reproduce the observed conductance oscillations. A very remarkable feature of the simple theory developed here is the fact that the predictions depend mostly on very general facts, namely, the discrete nature of electric charge and quantum mechanics; other detailed features of the systems described enter as parameters of the system, such as capacities and inductances.     

Dissipative chaotic quantum maps: Expectation values, correlation functions and the invariant state

I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the Frobenius-Perron operator, if . Several consequences arise: the Wigner transform of the invariant density matrix is a smeared out version of the classical strange attractor; time dependent expectation values and correlation functions of observables can be evaluated via hybrid quantum-classical formulae in which the quantum character enters only via the initial Wigner function. If a classical phase-space distribution is chosen for the latter or if the map is iterated sufficiently many times the formulae become entirely classical, and powerful classical trace formulae apply. Received 7 October 1999     

Newton-Leibniz integration for ket-bra operators in quantum mechanics (IV)—Integrations within Weyl ordered product of operators and their applications

We show that the technique of integration within normal ordering of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480-494] applied to tackling Newton-Leibniz integration over ket-bra projection operators, can be generalized to the technique of integration within Weyl ordered product (IWWOP) of operators. The Weyl ordering symbol is introduced to find the Wigner operator’s Weyl ordering form Δ(p,q) =  δ(p − P)δ(q − Q) , and to find operators’ Weyl ordered expansion formula. A remarkable property is that Weyl ordering of operators is covariant under similarity transformation, so it has many applications in quantum statistics and signal analysis. Thus the invention of the IWWOP technique promotes the progress of Dirac’s symbolic method.     

Hartman effect in presence of Aharanov-Bohm flux

The Hartman effect for a tunnelling particle implies the independence of group delay time on the opaque barrier width with superluminal velocities as a consequence. This effect is further examined on a quantum ring geometry in the presence of Aharonov-Bohm flux. We show that while tunnelling through an opaque barrier, the group delay time for given incident energy becomes independent of the barrier thickness as well as the magnitude of the flux. The Hartman effect is thereby extended beyond one dimension in the presence of Aharonov-Bohm flux.     

An alternative quantum fidelity for mixed states of qudits

We give an alternative definition of quantum fidelity for two density operators on qudits in terms of their Hilbert-Schmidt inner product and their purity. It can be regarded as the well-defined operator fidelity for the two operators and satisfies all Jozsa's four axioms up to a normalization factor. This fidelity is not computationally demanding.