3,172 research outputs found
Decoherence and classical predictability of phase space histories
We consider the decoherence of phase space histories in a class of quantum
Brownian motion models, consisting of a particle moving in a potential
in interaction with a heat bath at temperature and dissipation gamma, in
the Markovian regime. The evolution of the density operator for this open
system is thus described by a non-unitary master equation. The phase space
histories of the system are described by a class of quasiprojectors.
Generalizing earlier results of Hagedorn and Omn\`es, we show that a phase
space projector onto a phase space cell is approximately evolved under
the master equation into another phase space projector onto the classical
dissipative evolution of , and with a certain amount of degradation due
to the noise produced by the environment. We thus show that histories of phase
space samplings approximately decohere, and that the probabilities for these
histories are peaked about classical dissipative evolution, with a width of
peaking depending on the size of the noise.Comment: 34 pages, LATEX, revised version to avoid LATEX error
Spin-orbit coupling and electron spin resonance for interacting electrons in carbon nanotubes
We review the theoretical description of spin-orbit scattering and electron
spin resonance in carbon nanotubes. Particular emphasis is laid on the effects
of electron-electron interactions. The spin-orbit coupling is derived, and the
resulting ESR spectrum is analyzed both using the effective low-energy field
theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard
ladders. For single-wall tubes, the field theoretical description predicts a
double peak spectrum linked to the existence of spin-charge separation. The
numerical analysis basically confirms this picture, but also predicts
additional features in finite-size samples.Comment: 19 pages, 4 figures, invited review article for special issue in J.
Phys. Cond. Mat., published versio
Current-voltage scaling of chiral and gauge-glass models of two-dimensional superconductors
The scaling behavior of the current-voltage characteristics of chiral and
gauge glass models of disordered superconductors, are studied numerically, in
two dimensions. For both models, the linear resistance is nonzero at finite
temperatures and the scaling analysis of the nonlinear resistivity is
consistent with a phase transition at T=0 temperature characterized by a
diverging correlation length and thermal critical
exponent . The values of , however, are found to be different
for the chiral and gauge glass models, suggesting different universality
classes, in contrast to the result obtained recently in three dimensions.Comment: 4 pages, 4 figures (included), to appear in Phys. Rev.
Velocity quantization approach of the one-dimensional dissipative harmonic oscillator
Given a constant of motion for the one-dimensional harmonic oscillator with
linear dissipation in the velocity, the problem to get the Hamiltonian for this
system is pointed out, and the quantization up to second order in the
perturbation approach is used to determine the modification on the eigenvalues
when dissipation is taken into consideration. This quantization is realized
using the constant of motion instead of the Hamiltonian.Comment: 10 pages, 2 figure
Unstable decay and state selection II
The decay of unstable states when several metastable states are available for
occupation is investigated using path-integral techniques. Specifically, a
method is described which allows the probabilities with which the metastable
states are occupied to be calculated by finding optimal paths, and fluctuations
about them, in the weak noise limit. The method is illustrated on a system
described by two coupled Langevin equations, which are found in the study of
instabilities in fluid dynamics and superconductivity. The problem involves a
subtle interplay between non-linearities and noise, and a naive approximation
scheme which does not take this into account is shown to be unsatisfactory. The
use of optimal paths is briefly reviewed and then applied to finding the
conditional probability of ending up in one of the metastable states, having
begun in the unstable state. There are several aspects of the calculation which
distinguish it from most others involving optimal paths: (i) the paths do not
begin and end on an attractor, and moreover, the final point is to a large
extent arbitrary, (ii) the interplay between the fluctuations and the leading
order contribution are at the heart of the method, and (iii) the final result
involves quantities which are not exponentially small in the noise strength.
This final result, which gives the probability of a particular state being
selected in terms of the parameters of the dynamics, is remarkably simple and
agrees well with the results of numerical simulations. The method should be
applicable to similar problems in a number of other areas such as state
selection in lasers, activationless chemical reactions and population dynamics
in fluctuating environments.Comment: 28 pages, 6 figures. Accepted for publication in Phys. Rev.
Wigner Distribution Function Approach to Dissipative Problems in Quantum Mechanics with emphasis on Decoherence and Measurement Theory
We first review the usefulness of the Wigner distribution functions (WDF),
associated with Lindblad and pre-master equations, for analyzing a host of
problems in Quantum Optics where dissipation plays a major role, an arena where
weak coupling and long-time approximations are valid. However, we also show
their limitations for the discussion of decoherence, which is generally a
short-time phenomenon with decay rates typically much smaller than typical
dissipative decay rates. We discuss two approaches to the problem both of which
use a quantum Langevin equation (QLE) as a starting-point: (a) use of a reduced
WDF but in the context of an exact master equation (b) use of a WDF for the
complete system corresponding to entanglement at all times
Multiple Functionality in Nanotube Transistors
Calculations of quantum transport in a carbon nanotube transistor show that
such a device offers unique functionality. It can operate as a ballistic
field-effect transistor, with excellent characteristics even when scaled to 10
nm dimensions. At larger gate voltages, channel inversion leads to resonant
tunneling through an electrostatically defined nanoscale quantum dot. Thus the
transistor becomes a gated resonant tunelling device, with negative
differential resistance at a tunable threshold. For the dimensions considered
here, the device operates in the Coulomb blockade regime, even at room
temperature.Comment: To appear in Phys. Rev. Let
STOCHASTIC DYNAMICS OF LARGE-SCALE INFLATION IN DE~SITTER SPACE
In this paper we derive exact quantum Langevin equations for stochastic
dynamics of large-scale inflation in de~Sitter space. These quantum Langevin
equations are the equivalent of the Wigner equation and are described by a
system of stochastic differential equations. We present a formula for the
calculation of the expectation value of a quantum operator whose Weyl symbol is
a function of the large-scale inflation scalar field and its time derivative.
The unique solution is obtained for the Cauchy problem for the Wigner equation
for large-scale inflation. The stationary solution for the Wigner equation is
found for an arbitrary potential. It is shown that the large-scale inflation
scalar field in de Sitter space behaves as a quantum one-dimensional
dissipative system, which supports the earlier results. But the analogy with a
one-dimensional model of the quantum linearly damped anharmonic oscillator is
not complete: the difference arises from the new time dependent commutation
relation for the large-scale field and its time derivative. It is found that,
for the large-scale inflation scalar field the large time asymptotics is equal
to the `classical limit'. For the large time limit the quantum Langevin
equations are just the classical stochastic Langevin equations (only the
stationary state is defined by the quantum field theory).Comment: 21 pages RevTex preprint styl
Charge Screening Effect in Metallic Carbon Nanotubes
Charge screening effect in metallic carbon nanotubes is investigated in a
model including the one-dimensional long-range Coulomb interaction. It is
pointed out that an external charge which is being fixed spatially is screened
by internal electrons so that the resulting object becomes electrically
neutral. We found that the screening length is given by about the diameter of a
nanotube.Comment: 11 pages, 6 figure
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