2,703 research outputs found
Lorentz Transformation of Blackbody Radiation
We present a simple calculation of the Lorentz transformation of the spectral
distribution of blackbody radiation at temperature T. Here we emphasize that T
is the temperature in the blackbody rest frame and does not change. We thus
avoid the confused and confusing question of how temperature transforms. We
show by explicit calculation that at zero temperature the spectral distribution
is invariant. At finite temperature we find the well known result familiar in
discussions of the the 2.7! K cosmic radiation.Comment: 6 page
A pair of oscillators interacting with a common heat bath
Here the problem considered is that of a pair of oscillators coupled to a
common heat bath. Many, if not most, discussions of a single operator coupled
to a bath have used the independent oscillator model of the bath. However, that
model has no notion of separation, so the question of phenomena when the
oscillators are near one another compared with when they are widely separated
cannot be addressed. Here the Lamb model of an oscillator attached to a
stretched string is generalized to illustrate some of these questions. The
coupled Langevin equations for a pair of oscillators attached to the string at
different points are derived and their limits for large and small separations
obtained. Finally, as an illustration of a different phenomenon, the
fluctuation force between a pair of masses attached to the string is
calculated, with closed form expressions for the force at small and large
separations
Wave Packet Spreading: Temperature and Squeezing Effects with Applications to Quantum Measurement and Decoherence
A localized free particle is represented by a wave packet and its motion is
discussed in most quantum mechanics textbooks. Implicit in these discussions is
the assumption of zero temperature. We discuss how the effects of finite
temperature and squeezing can be incorporated in an elementary manner. The
results show how the introduction of simple tools and ideas can bring the
reader into contact with topics at the frontiers of research in quantum
mechanics. We discuss the standard quantum limit, which is of interest in the
measurement of small forces, and decoherence of a mixed (``Schrodinger cat'')
state, which has implications for current research in quantum computation,
entanglement, and the quantum-classical interface
Wigner Distribution Analysis of a Schrodinger Cat Superposition of Displaced Equilibrium Coherent States
Motivated by recent experiments, we consider a Schr\"{o}dinger cat
superposition of two widely separated coherent states in thermal equilibrium.
The time development of our system is obtained using Wigner distribution
functions. In contrast to our discussion for a two-Gaussian wave packet [Phys.
Lett. A 286 (2001) 87], we find that, in the absence of dissipation, the
interference term does not decay rapidly in time, but in common with the other
two terms, it oscillates in time and persists for all timesComment: Proc. of Wigner Centennial Conferenc
Quantum thermodynamic functions for an oscillator coupled to a heat bath
Small systems (of interest in the areas of nanophysics, quantum information,
etc.) are particularly vulnerable to environmental effects. Thus, we determine
various thermodynamic functions for an oscillator in an arbitrary heat bath at
arbitrary temperatures. Explicit results are presented for the most commonly
discussed heat bath models: Ohmic, single relaxation time and blackbody
radiation.Comment: Phys. Rev. B, in pres
Exact analysis of disentanglement for continuous variable systems and application to a two-body system at zero temperature in an arbitrary heat bath
We outline an exact approach to decoherence and entanglement problems for
continuous variable systems. The method is based on a construction of quantum
distribution functions introduced by Ford and Lewis \cite{ford86} in which a
system in thermal equilibrium is placed in an initial state by a measurement
and then sampled by subsequent measurements. With the Langevin equation
describing quantum Brownian motion, this method has proved to be a powerful
tool for discussing such problems. After reviewing our previous work on
decoherence and our recent work on disentanglement, we apply the method to the
problem of a pair of particles in a correlated Gaussian state. The initial
state and its time development are explicitly exhibited. For a single
relaxation time bath at zero temperature exact numerical results are given. The
criterion of Duan et al. \cite{duan00} for such states is used to prove that
the state is initially entangled and becomes separable after a finite time
(entanglement sudden death)
Decoherence in Phase Space
Much of the discussion of decoherence has been in terms of a particle moving
in one dimension that is placed in an initial superposition state (a
Schr\"{o}dinger "cat" state) corresponding to two widely separated wave
packets. Decoherence refers to the destruction of the interference term in the
quantum probability function. Here, we stress that a quantitative measure of
decoherence depends not only on the specific system being studied but also on
whether one is considering coordinate, momentum or phase space. We show that
this is best illustrated by considering Wigner phase space where the measure is
again different. Analytic results for the time development of the Wigner
distribution function for a two-Gaussian Schrodinger "cat" state have been
obtained in the high-temperature limit (where decoherence can occur even for
negligible dissipation) which facilitates a simple demonstration of our
remarks.Comment: in press in Laser Phys.13(2003
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