3,440 research outputs found
Schulman Replies
This is a reply to a comment of Casati, Chirikov and Zhirov (PRL 85, 896
(2000)) on PRL 83, 5419 (1999).
The suitability of the particlar two-time boundary value problem used in the
earlier PRL is argued
Opposite Thermodynamic Arrows of Time
A model in which two weakly coupled systems maintain opposite running
thermodynamic arrows of time is exhibited. Each experiences its own retarded
electromagnetic interaction and can be seen by the other. The possibility of
opposite-arrow systems at stellar distances is explored and a relation to dark
matter suggested.Comment: To appear in Phys. Rev. Let
Imaging geometry through dynamics: the observable representation
For many stochastic processes there is an underlying coordinate space, ,
with the process moving from point to point in or on variables (such as
spin configurations) defined with respect to . There is a matrix of
transition probabilities (whether between points in or between variables
defined on ) and we focus on its ``slow'' eigenvectors, those with
eigenvalues closest to that of the stationary eigenvector. These eigenvectors
are the ``observables,'' and they can be used to recover geometrical features
of
Relative momentum for identical particles
Possible definitions for the relative momentum of identical particles are
considered
Analysis of a three-component model phase diagram by Catastrophe Theory
We analyze the thermodynamical potential of a lattice gas model with three
components and five parameters using the methods of Catastrophe Theory. We find
the highest singularity, which has codimension five, and establish its
transversality. Hence the corresponding seven-degree Landau potential, the
canonical form Wigwam or , constitutes the adequate starting point to
study the overall phase diagram of this model.Comment: 16 pages, Latex file, submitted to Phys. Rev.
Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities
The phenomenology of quantum systems in curved space-times is among the most
fascinating fields of physics, allowing --often at the gedankenexperiment
level-- constraints on tentative theories of quantum gravity. Determining the
dynamics of fields in curved backgrounds remains however a complicated task
because of the highly intricate partial differential equations involved,
especially when the space metric exhibits no symmetry. In this article, we
provide --in a pedagogical way-- a general formalism to determine this dynamics
at the semiclassical order. To this purpose, a generic expression for the
semiclassical propagator is computed and the equation of motion for the
probability four-current is derived. Those results underline a direct analogy
between the computation of the propagator in general relativistic quantum
mechanics and the computation of the propagator for stationary systems in
non-relativistic quantum mechanics. A possible application of this formalism to
curvature-induced quantum interferences is also discussed.Comment: New materials on gravitationally-induced quantum interferences has
been adde
Semi-optimal Practicable Algorithmic Cooling
Algorithmic Cooling (AC) of spins applies entropy manipulation algorithms in
open spin-systems in order to cool spins far beyond Shannon's entropy bound. AC
of nuclear spins was demonstrated experimentally, and may contribute to nuclear
magnetic resonance (NMR) spectroscopy. Several cooling algorithms were
suggested in recent years, including practicable algorithmic cooling (PAC) and
exhaustive AC. Practicable algorithms have simple implementations, yet their
level of cooling is far from optimal; Exhaustive algorithms, on the other hand,
cool much better, and some even reach (asymptotically) an optimal level of
cooling, but they are not practicable. We introduce here semi-optimal
practicable AC (SOPAC), wherein few cycles (typically 2-6) are performed at
each recursive level. Two classes of SOPAC algorithms are proposed and
analyzed. Both attain cooling levels significantly better than PAC, and are
much more efficient than the exhaustive algorithms. The new algorithms are
shown to bridge the gap between PAC and exhaustive AC. In addition, we
calculated the number of spins required by SOPAC in order to purify qubits for
quantum computation. As few as 12 and 7 spins are required (in an ideal
scenario) to yield a mildly pure spin (60% polarized) from initial
polarizations of 1% and 10%, respectively. In the latter case, about five more
spins are sufficient to produce a highly pure spin (99.99% polarized), which
could be relevant for fault-tolerant quantum computing.Comment: 13 pages, 5 figure
Passage-time distributions from a spin-boson detector model
The passage-time distribution for a spread-out quantum particle to traverse a
specific region is calculated using a detailed quantum model for the detector
involved. That model, developed and investigated in earlier works, is based on
the detected particle's enhancement of the coupling between a collection of
spins (in a metastable state) and their environment. We treat the continuum
limit of the model, under the assumption of the Markov property, and calculate
the particle state immediately after the first detection. An explicit example
with 15 boson modes shows excellent agreement between the discrete model and
the continuum limit. Analytical expressions for the passage-time distribution
as well as numerical examples are presented. The precision of the measurement
scheme is estimated and its optimization discussed. For slow particles, the
precision goes like , which improves previous estimates,
obtained with a quantum clock model.Comment: 11 pages, 6 figures; minor changes, references corrected; accepted
for publication in Phys. Rev.
Observing trajectories with weak measurements in quantum systems in the semiclassical regime
We propose a scheme allowing to observe the evolution of a quantum system in
the semiclassical regime along the paths generated by the propagator. The
scheme relies on performing consecutive weak measurements of the position. We
show how weak trajectories" can be extracted from the pointers of a series of
measurement devices having weakly interacted with the system. The properties of
these "weak trajectories" are investigated and illustrated in the case of a
time-dependent model system.Comment: v2: Several minor corrections were made. Added Appendix (that will
appear as Suppl. Material). To be published in Phys Rev Let
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