Quantum Dynamics Of Particles Research Articles

Self‐similar wavepackets for describing warm dense matter

AbstractUsing the time dependent variational principle, we develop a general formulation of single particle quantum dynamics within the assumption that the wavepacket's density remains self‐similar. We obtain the amplitudephase relationship from the continuity equation. We investigate the ground state properties of waves with Gaussian and exponential densities in hydrogenic and helium‐like systems. We show that the exponential wavepackets yield superior ground state energies ‐ an important advantage in describing warm dense matter (T < 50 eV) in which bound states form. Exponentials yield an improved ground state energy for molecular hydrogen, but with a bond length 13% short of the experimental value. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Quantum ratchets and quantum heat pumps

Quantum ratchets are Brownian motors in which the quantum dynamics of particles induces qualitatively new behavior. We review a series of experiments in which asymmetric semiconductor devices of sub-micron dimensions are used to study quantum ratchets for electrons. In rocked quantum-dot ratchets electron-wave interference is used to create a non-linear voltage response, leading to a ratchet effect. The direction of the net ratchet current in this type of device can be sensitively controlled by changing one of the following experimental variables: a small external magnetic field, the amplitude of the rocking force, or the Fermi energy. We also describe a tunneling ratchet in which the current direction depends on temperature. In our discussion of the tunneling ratchet we distinguish between three contributions to the non-linear current–voltage characteristics that lead to the ratchet effect: thermal excitation over energy barriers, tunneling through barriers, and wave reflection from barriers. Finally, we discuss the operation of adiabatically rocked tunneling ratchets as heat pumps.

Quantum Brownian motion in ratchet potentials

We investigate the dynamics of quantum particles in a ratchet potential subject to an ac force field. We develop a perturbative approach for weak ratchet potentials and force fields. Within this approach, we obtain an analytic description of dc current rectification and current reversals. Transport characteristics for various limiting cases -- such as the classical limit, limit of high or low frequencies, and/or high temperatures -- are derived explicitly. To gain insight into the intricate dependence of the rectified current on the relevant parameters, we identify characteristic scales and obtain the response of the ratchet system in terms of scaling functions. We pay a special attention to inertial effects and show that they are often relevant, for example, at high temperatures. We find that the high temperature decay of the rectified current follows an algebraic law with a non-trivial exponent, $j\propto T^{-17/6}$.

Supersymmetry-Based Approach to Quantum Particle Dynamics on a Curved Surface with Non-zero Magnetic Field

We present the N=2 supersymmetric formulation for the classical and quantum dynamics of a nonrelativistic charged particle on a curved surface in the presence of a perpendicular magnetic field. For a particle moving on a constant-curvature surface in a constant magnetic field, our Hamiltonian possesses the shape-invariance property in addition. On the surface of a sphere and also on the hyperbolic plane, we exploit the supersymmetry and shape-invariance properties to obtain complete solutions to the corresponding quantum mechanical problems.

Dynamics of quantum particles by path-integral centroid simulations: The symmetric Eckart barrier

The path-integral centroid approach has been applied to study the dynamical properties of a flux of protons impinging on a symmetric Eckart barrier. The mean transmission coefficient, transmitted flux, and kinetic energy of transmitted particles have been calculated by path-integral centroid simulations as a function of temperature, and compared to exact results obtained from the solution of the Schrödinger equation. The studied temperatures cover the crossover from a classical regime, where the barrier crossing is thermally activated, to a quantum regime, where the barrier crossing is dominated by tunneling of low energy particles. We show, in agreement with previous studies, that the centroid density is a central quantity to derive dynamical properties. Moreover, we find that the equilibrium internal energy obtained for the centroid fixed at the barrier top, reproduces closely the difference between the mean kinetic energy of transmitted and incident particles, and it can be used to define a velocity (pre-exponential) factor that improves previous approximations to the transmitted flux, in the whole temperature range above and below the classical-quantum crossover.

Quantum transport properties of composite materials by generalized molecular dynamics method in Wigner formulation of quantum mechanics

A new method for solving Wigner-Liouville-type equations and studying dynamics of quantum particles in composite materials and disordered system of scatterershas been developed. Approach combines both molecular dynamics and Monte Carlo methods. Numerical results have been obtained for the frequency dependences of tensors of electron conductivity and permitivity according to quantum Kubo formulas.

Quantum probes of spacetime singularities.

It is shown that there are static spacetimes with timelike curvature singularities which appear completely nonsingular when probed with quantum test particles. Examples include extreme dilatonic black holes and the fundamental string solution. In these spacetimes, the dynamics of quantum particles is well defined and uniquely determined.

Generalized antinormally ordered quantum phase-space distribution functions.

A class of positive quantum phase-space distributions based on antinormal ordering of the squeezed-photon annihilation and creation operators is introduced. This class of distributions, referred to as the generalized antinormally ordered distributions, is shown to be generated when the Wigner distribution is smoothed with a squeezed Gaussian wave packet. The distribution function associated with generalized antinormal ordering can thus be identified as the Husimi distribution function. The usefulness of the distributions in studies of the quantum particle dynamics is illustrated with simple examples.

RELATIVISTIC SPIN 1/2 PARTICLE ON THE TOTAL SPACE OF U(1)-MONOPOLE BUNDLE

A relativistic spin 1/2 particle quantum dynamics on the total space P of principle bundle, which is commonly attributed to Dirac monopole, is described. This dynamics is completely characterized with the help of additional U (1)-bundle P* which turned out to be connected with scattering problem. We formulate the representation in which the Hamiltonian has the most simple form. Lift of the Lorentz group to the total space is constructed.

Self-consistent Monte Carlo particle transport with model quantum tunneling dynamics: Application to the intrinsic bistability of a symmetric double-barrier structure

The intrinsic bistability in a symmetric resonant tunneling device (RTD) is simulated by the ensemble particle Monte Carlo technique, coupled with a simple model of the space- and time-dependent particle quantum dynamics inside the double-barrier region of the RTD. This model particle quantum dynamics is based upon the phase-time delay, which is obtained from a piecewise-linear-potential Airy function approach to the calculation of the transmission amplitude. An unambiguous hysteresis in the negative differential resistance (NDR) region of the current-voltage (I-V) characteristic is observed for a symmetric AlGaAs/GaAs double-barrier structure. The dynamical accumulation of carriers in the well is seen to be the cause of this marked bistability/hysteresis. However, the plateau-like features of the I-V curve are not resolved, although oscillations in the quantum well carrier density in the NDR are prominent. This article strongly suggests that a more accurate treatment of the space- and time-dependent particle quantum dynamics across the RTD is of paramount importance.

Lattice Weyl-Wigner formulation of exact many-body quantum-transport theory and applications to novel solid-state quantum-based devices.

The use of the lattice-space Weyl-Wigner formalism of the quantum dynamics of particles in solids, coupled with nonequilibrium Green's-function techniques, provides a rigorous and straightforward derivation of an exact integral form of the equation for a quantum distribution function in many-body quantum-transport theory. We show that with the present formalism more realistic calculations, both numerical (particularly, highly transient simulations) and analytical (fully gauge-invariant calculations), which include full quantum effects and many-body effects, can be carried out in a straightforward, elegant, and physically meaningful manner. This is demonstrated by new results based on a more-accurate numerical simulation procedure and novel applications in terms of ``quantum particle trajectories'' for resonant tunneling diodes, and by a straightforward and fully gauge-invariant formulation of the exact quantum-transport equation of a uniform electron-phonon scattering system in high electric fields, which, for the first time, do not involve any gradient expansion.

On the quantum theory of electron transport in the Wigner formalism

The use of a lattice-space Weyl–Wigner formalism of quantum dynamics of particles in solids, coupled with the nonequilibrium Green’s function technique, provides a rigorous and straightforward derivation of an exact integral form of the equation for a quantum-distribution function in many-body quantum transport theory. This formulation leads to a straightforward and fully gauge-invariant derivation of the exact quantum transport equation of a uniform electron-phonon scattering system in high electric fields which do not involve any gradient expansion. The resulting expressions serve to generalize previous results.

Stationary regime for the quantum dynamics of particles in a randomly varying potential

Stationary regime for the quantum dynamics of particles in a randomly varying potential

Unitary Representations of the Lorentz Group and Particle Dynamics

We examine the quantum dynamics of particles with arbitrary spin implied by explicit use of the infinite dimensional unitary representation of the Lorentz group, introduced by Majorana. Comparison with the classical theory of spinning particles shows that this unitary representation leads to a quantum mechanical analog of the relativistic pure gyroscope.