38 research outputs found
An analytic study of the ionization from an ultrathin quantum well in a weak electrostatic field
We consider the time evolution of a particle bound by an attractive
one-dimensional delta-function potential (at x = 0) when a uniform
electrostatic field (F) is applied. We explore explicit expressions for the
time-dependent wavefunction \psi_F(x,t) and the ionization probability
{\mathcal{P}}(t), respectively, in the weak-field limit. In doing so,
\psi_F(0,t) is a key element to their evaluation. We obtain a closed expression
for \psi_F(0,t) which is an excellent approximation of the exact result being a
numerical solution of the Lippmann-Schwinger integral equation. The resulting
probability density |\psi_F(0,t)|^2, as a simple alternative to
{\mathcal{P}}(t), is also in good agreement to its counterpart from the exact
one. In doing this, we also find a new and useful integral identity of the Airy
function.Comment: 3 figure
Jarzynski equality and the second law of thermodynamics beyond the weak-coupling limit: The quantum Brownian oscillator
We consider a time-dependent quantum linear oscillator coupled to a bath at
an arbitrary strength. We then introduce a generalized Jarzynski equality (GJE)
which includes the terms reflecting the system-bath coupling. This enables us
to study systematically the coupling effect on the linear oscillator in a
non-equilibrium process. This is also associated with the second law of
thermodynamics beyond the weak-coupling limit. We next take into consideration
the GJE in the classical limit. By this generalization we show that the
Jarzynski equality in its original form can be associated with the second law,
in both quantal and classical domains, only in the vanishingly small coupling
regime.Comment: 7 figure
Electrostatic-field-induced dynamics in an ultrathin quantum well
We consider the time evolution of a particle subjected to both a uniform
electrostatic field F and a one-dimensional delta-function potential well. We
derive the propagator K_F(x,t|x',0) of this system, directly leading to the
wavefunction psi_F(x,t), in which its essential ingredient K_F(0,t|0,0),
accounting for the ionization-recombination in the bound-continuum transition,
is exactly expressed in terms of the multiple hypergeometric functions
F(z_1,z_2,...,z_n). And then we obtain the ingredient K_F(0,t|0,0) in an
appropriate approximation scheme, expressed in terms of the generalized
hypergeometric functions p_F_q(z) being much more transparent to physically
interpret and much more accessible in their numerical evaluation than the
functions F(z_1,z_2,...,z_n).Comment: 24 pages, 1 figur
Non-negative Wigner-like distributions and Renyi-Wigner entropies of arbitrary non-Gaussian quantum states: The thermal state of the one-dimensional box problem
In this work, we consider the phase-space picture of quantum mechanics. We
then introduce non-negative Wigner-like (operational) distributions
\widetilde{\mathcal W}_{rho;alpha}(x,p) corresponding to the density operator
\hat{rho} and being proportional to {W_{rho^(alpha/2)}(x,p)}^2, where
W_{rho}(x,p) denotes the usual Wigner function. In doing so, we utilize the
formal symmetry between the purity measure Tr(rho^2) and its Wigner
representation (2 pi hbar) \int dx dp {W_{rho}(x,p)}^2 and then consider, as a
generalization, such symmetry between the fractional moment
Tr(\hat{rho}^{alpha}) and its Wigner representation (2 pi hbar) \int dx dp
{W_{rho^{alpha/2}}(x,p)}^2. Next, we create a framework that enables explicit
evaluation of the Renyi-Wigner entropies for the classical-like distributions
\widetilde{\mathcal W}_{rho;alpha}(x,p). Consequently, a better understanding
of some non-Gaussian features of a given state rho will be given, by comparison
with the Gaussian state rho_G defined in terms of its Wigner function
W_{rho_G}(x,p) and essentially determined by its purity measure T(rho_G)^2
alone. To illustrate the validity of our framework, we evaluate the
distributions \widetilde{\mathcal W}_{beta;alpha}(x,p) corresponding to the
(non-Gaussian) thermal state rho_{\beta} of a single particle confined by a
one-dimensional infinite potential well with either the Dirichlet or Neumann
boundary condition and then analyze the resulting Renyi entropies. Our
phase-space approach will also contribute to a deeper understanding of
non-Gaussian states and their properties either in the semiclassical limit
(hbar \to 0) or in the high-temperature limit (beta \to 0), as well as enabling
us to systematically discuss the quantal-classical Second Law of Thermodynamics
on the single footing.Comment: 27 pages, 6 figure
Moving quantum agents in a finite environment
We investigate an all-quantum-mechanical spin network, in which a subset of
spins, the ``moving agents'', are subject to local and pair unitary
transformations controlled by their position with respect to a fixed ring of
``environmental''-spins. We demonstrate that a ``flow of coherence''
results between the various subsystems. Despite entanglement between the agents
and between agent and environment, local (non-linear) invariants may persist,
which then show up as fascinating patterns in each agent's Bloch-sphere. Such
patterns disappear, though, if the agents are controlled by different rules.
Geometric aspects thus help to understand the interplay between entanglement
and decoherence.Comment: REVTEX, to appear in Proceedings of Decoherence Workshop, Bielefeld,
199
Quantum chaos in small quantum networks
We study a 2-spin quantum Turing architecture, in which discrete local
rotations \alpha_m of the Turing head spin alternate with quantum controlled
NOT-operations. We show that a single chaotic parameter input \alpha_m leads to
a chaotic dynamics in the entire Hilbert space. The instability of periodic
orbits on the Turing head and `chaos swapping' onto the Turing tape are
demonstrated explicitly as well as exponential parameter sensitivity of the
Bures metric.Comment: Accepted for publication in JMO (quantum information special issue,
Vol 47), 3 figure
The Clausius inequality beyond the weak coupling limit: The quantum Brownian oscillator revisited
We consider a quantum linear oscillator coupled at an arbitrary strength to a
bath at an arbitrary temperature. We find an exact closed expression for the
oscillator density operator. This state is non-canonical but can be shown to be
equivalent to that of an uncoupled linear oscillator at an effective
temperature T_{eff} with an effective mass and an effective spring constant. We
derive an effective Clausius inequality delta Q_{eff} =< T_{eff} dS, where
delta Q_{eff} is the heat exchanged between the effective (weakly coupled)
oscillator and the bath, and S represents a thermal entropy of the effective
oscillator, being identical to the von-Neumann entropy of the coupled
oscillator. Using this inequality (for a cyclic process in terms of a variation
of the coupling strength) we confirm the validity of the second law. For a
fixed coupling strength this inequality can also be tested for a process in
terms of a variation of either the oscillator mass or its spring constant. Then
it is never violated. The properly defined Clausius inequality is thus more
robust than assumed previously.Comment: 30 pages, 7 figure
Renyi-alpha entropies of quantum states in closed form: Gaussian states and a class of non-Gaussian states
In this work, we study the Renyi-alpha entropies S_{alpha}(\hat{rho}) = (1 -
alpha)^{-1} \ln{Tr(\hat{rho}^{alpha})} of quantum states for N bosons in the
phase-space representation. With the help of the Bopp rule, we derive the
entropies of Gaussian states in closed form for positive integers alpha =
2,3,4, ... and then, with the help of the analytic continuation, acquire the
closed form also for real values of alpha > 0. The quantity S_2(\hat{rho}),
primarily studied in the literature, will then be a special case of our
finding. Subsequently we acquire the Renyi-alpha entropies, with positive
integers alpha, in closed form also for a specific class of the non-Gaussian
states (mixed states) for N bosons, which may be regarded as a generalization
of the eigenstates |n> (pure states) of a single harmonic oscillator with n >=
1, in which the Wigner functions have negative values indeed. Due to the fact
that the dynamics of a system consisting of oscillators is Gaussian, our
result will contribute to a systematic study of the Renyi-alpha entropy
dynamics when the current form of a non-Gaussian state is initially prepared.Comment: Accepted for publication in Physical Review
Comment on the quantum nature of angular momentum using a coupled-boson representation
A simple approach for understanding the quantum nature of angular momentum
and its reduction to the classical limit is presented based on Schwinger's
coupled-boson representation. This approach leads to a straightforward
explanation of why the square of the angular momentum in quantum mechanics is
given by j(j+1) instead of just j^2, where j is the angular momentum quantum
number
Ab initio relaxation times and time-dependent Hamiltonians within the steepest-entropy-ascent quantum thermodynamic framework
Quantum systems driven by time-dependent Hamiltonians are considered here
within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT)
and used to study the thermodynamic characteristics of such systems. In doing
so, a generalization of the SEAQT framework valid for all such systems is
provided, leading to the development of an ab initio physically relevant
expression for the intra-relaxation time, an important element of this
framework and one that had as of yet not been uniquely determined as an
integral part of the theory. The resulting expression for the relaxation time
is valid as well for time-independent Hamiltonians as a special case and makes
the description provided by the SEAQT framework more robust at the fundamental
level. In addition, the SEAQT framework is used to help resolve a fundamental
issue of thermodynamics in the quantum domain, namely, that concerning the
unique definition of process-dependent work and heat functions. The
developments presented lead to the conclusion that this framework is not just
an alternative approach to thermodynamics in the quantum domain but instead one
that uniquely sheds new light on various fundamental but as of yet not
completely resolved questions of thermodynamics.Comment: Accepted for publication in Physical Review