186 research outputs found
Relation between phase space coverage and entanglement for spin-1/2 systems
For systems of two and three spins 1/2 it is known that the second moment of
the Husimi function can be related to entanglement properties of the
corresponding states. Here, we generalize this relation to an arbitrary number
of spins in a pure state. It is shown that the second moment of the Husimi
function can be expressed in terms of the lengths of the concurrence vectors
for all possible partitions of the N-spin system in two subsystems. This
relation implies that the phase space distribution of an entangled state is
less localized than that of a non-entangled state. As an example, the second
moment of the Husimi function is analyzed for an Ising chain subject to a
magnetic field perpendicular to the chain axis.Comment: 6 pages, 2 figures, RevTeX forma
Fundamental Aspects of Quantum Brownian Motion
With this work we elaborate on the physics of quantum noise in thermal
equilibrium and in stationary non-equilibrium. Starting out from the celebrated
quantum fluctuation-dissipation theorem we discuss some important consequences
that must hold for open, dissipative quantum systems in thermal equilibrium.
The issue of quantum dissipation is exemplified with the fundamental problem of
a damped harmonic quantum oscillator. The role of quantum fluctuations is
discussed in the context of both, the nonlinear generalized quantum Langevin
equation and the path integral approach. We discuss the consequences of the
time-reversal symmetry for an open dissipative quantum dynamics and,
furthermore, point to a series of subtleties and possible pitfalls. The path
integral methodology is applied to the decay of metastable states assisted by
quantum Brownian noise.Comment: 13 pages, 4 figures, RevTeX, submitted to Chaos special issue "100
Years of Brownian Motion
Effect of zero point phase fluctuations on Josephson tunneling
In the presence of phase fluctuations the dc Josephson effect is modified and
the supercurrent at zero voltage is replaced by a peak at small but finite
voltages. It is shown that at zero temperature this peak is determined by two
complementary expansions of finite radius of convergence. The leading order
expressions are related to results known from the regimes of Coulomb blockade
and of macroscopic quantum tunneling. The peak positions and the suppression of
the critical current by quantum fluctuations are discussed.Comment: 4 pages, 4 figures, RevTe
Quantum dissipative Brownian motion and the Casimir effect
We explore an analogy between the thermodynamics of a free dissipative
quantum particle and that of an electromagnetic field between two mirrors of
finite conductivity. While a free particle isolated from its environment will
effectively be in the high-temperature limit for any nonvanishing temperature,
a finite coupling to the environment leads to quantum effects ensuring the
correct low-temperature behavior. Even then, it is found that under appropriate
circumstances the entropy can be a nonmonotonic function of the temperature.
Such a scenario with its specific dependence on the ratio of temperature and
damping constant also appears for the transverse electric mode in the Casimir
effect. The limits of vanishing dissipation for the quantum particle and of
infinite conductivity of the mirrors in the Casimir effect both turn out to be
noncontinuous.Comment: 13 pages, 8 figure
Thermodynamic anomalies in the presence of dissipation: from the free particle to the harmonic oscillator
A free particle coupled to a heat bath can exhibit a number of thermodynamic
anomalies like a negative specific heat or reentrant classicality. These
low-temperature phenomena are expected to be modified at very low temperatures
where finite-size effects associated with the discreteness of the energy
spectrum become relevant. In this paper, we explore in which form the
thermodynamic anomalies of the free damped particle appear for a damped
harmonic oscillator. Since the discreteness of the oscillator's energy spectrum
is fully accounted for, the results are valid for arbitrary temperatures. As
expected, they are in agreement with the third law of thermodynamics and
indicate how the thermodynamic anomalies of the free damped particle can be
reconciled with the third law. Particular attention is paid to the transition
from the harmonic oscillator to the free particle when the limit of the
oscillator frequency to zero is taken.Comment: 10 pages, 5 figure
Reentrant classicality of a damped system
For a free particle, the coupling to its environment can be the relevant
mechanism to induce quantum behavior as the temperature is lowered. We study
general linear environments with a spectral density proportional to {\omega}^s
at low frequencies and consider in particular the specific heat of the free
damped particle. For super-Ohmic baths with s>=2, a reentrant classical
behavior is found. As the temperature is lowered, the specific heat decreases
from the classical value of k_B/2, thereby indicating the appearence of quantum
effects. However, the classical value of the specific heat is restored as the
temperature approaches zero. This surprising behavior is due to the suppressed
density of bath degrees of freedom at low frequencies. For s<2, the specific
heat at zero temperature increases linearly with s from -k_B/2 to k_B/2. An
Ohmic bath, s=1, is thus very special in the sense that it represents the only
case where the specific heat vanishes at zero temperature.Comment: 6 pages, 3 figure
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