1,759 research outputs found
Equilibrium states and their entropy densities in gauge-invariant C*-systems
A gauge-invariant C*-system is obtained as the fixed point subalgebra of the
infinite tensor product of full matrix algebras under the tensor product
unitary action of a compact group. In the paper, thermodynamics is studied on
such systems and the chemical potential theory developed by Araki, Haag,
Kastler and Takesaki is used. As a generalization of quantum spin system, the
equivalence of the KMS condition, the Gibbs condition and the variational
principle is shown for translation-invariant states. The entropy density of
extremal equilibrium states is also investigated in relation to macroscopic
uniformity.Comment: 20 pages, revised in March 200
Off-Diagonal Long-Range Order: Meissner Effect and Flux Quantization
There has been a proof by Sewell that the hypothesis of off-diagonal
long-range order in the reduced density matrix implies the Meissner
effect. We present in this note an elementary and straightforward proof that
not only the Meissner effect but also the property of magnetic flux
quantization follows from the hypothesis. It is explicitly shown that the two
phenomena are closely related, and phase coherence is the origin for both.Comment: 11 pages, Latex fil
On the Question of Temperature Transformations under Lorentz and Galilei Boosts
We provide a quantum statistical thermodynamical solution of the long
standing problem of temperature transformations of uniformly moving bodies. Our
treatment of this question is based on the well established quantum statistical
result that the thermal equilibrium conditions demanded by both the Zeroth and
Second Laws of Thermodynamics are precisely those of Kubo, Martin and Schwinger
(KMS). We prove that, in both the special relativistic and nonrelativistic
settings, a state of a body cannot satisfy these conditions for different
inertial frames with non-zero relative velocity. Hence a body that serves as a
thermal reservoir, in the sense of the Zeroth Law, in an inertial rest frame
cannot do so in a laboratory frame relative to which it moves with non-zero
uniform velocity. Consequently, there is no law of temperature transformation
under either Lorentz or Galilei boosts, and so the concept of temperature
stemming from the Zeroth Law is restricted to states of bodies in their rest
frames.Comment: A few minor corrections have been made. The article will be published
in J. Phys.
Off-Diagonal Long-Range Order in Bose Liquids: Irrotational Flow and Quantization of Circulation
On the basis of gauge invariance, it is proven in an elementary and
straightforward manner, but without invoking any {\it ad hoc} assumption, that
the existence of off-diagonal long-range order in one-particle reduced density
matrix in Bose liquids implies both the irrotational flow in a simply connected
region and the quantization of circulation in a multiply connected region, the
two fundamental properties of a Bose superfluid. The origin for both is the
phase coherence of condensate wave-functions. Some relevant issues are also
addressed.Comment: Revtex, 4 pages, no figure
A Comment on the Geometric Entropy and Conical Space
It has been recently pointed out that a definition of the geometric entropy
using the partition function in a conical space does not in general lead to a
positive definite quantity. For a scalar field model with a non-minimal
coupling we clarify the origin of the anomalous behavior from the viewpoint of
the canonical formulation.Comment: No Figures. To appear in Classical and Quantum Gravit
Analytic Evaluation of the Decay Rate for Accelerated Proton
We evaluate the decay rate of the uniformly accelerated proton. We obtain an
analytic expression for inverse beta decay process caused by the acceleration.
We evaluate the decay rate both from the inertial frame and from the
accelerated frame where we should consider thermal radiation by Unruh effect.
We explicitly check that the decay rates obtained in both frame coincide with
each other.Comment: 11 page
Correlated Wave-Functions and the Absence of Long Range Order in Numerical Studies of the Hubbard Model
We present a formulation of the Constrained Path Monte Carlo (CPMC) method
for fermions that uses trial wave-functions that include many-body effects.
This new formulation allows us to implement a whole family of generalized
mean-field states as constraints. As an example, we calculated superconducting
pairing correlation functions for the two-dimensional repulsive Hubbard model
using a BCS trial state as the constraint. We compared the results with the
case where a free-electron trial wave-function is used. We found that the
correlation functions are independent of which state is used as the constraint,
which reaffirms the results previously found by Zhang et. al regarding the
suppression of long range pairing correlations as the system size increases.Comment: 15 pages, 3 figures, submitted to Phys. Rev.
Is life a thermal horizon ?
This talk aims at questioning the vanishing of Unruh temperature for an
inertial observer in Minkovski spacetime with finite lifetime, arguing that in
the non eternal case the existence of a causal horizon is not linked to the
non-vanishing of the acceleration. This is illustrated by a previous result,
the diamonds temperature, that adapts the algebraic approach of Unruh effect to
the finite case.Comment: Proceedings of the conference DICE 2006, Piombino september 200
Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis
We study the Unruh effect for an observer with a finite lifetime, using the
thermal time hypothesis. The thermal time hypothesis maintains that: (i) time
is the physical quantity determined by the flow defined by a state over an
observable algebra, and (ii) when this flow is proportional to a geometric flow
in spacetime, temperature is the ratio between flow parameter and proper time.
An eternal accelerated Unruh observer has access to the local algebra
associated to a Rindler wedge. The flow defined by the Minkowski vacuum of a
field theory over this algebra is proportional to a flow in spacetime and the
associated temperature is the Unruh temperature. An observer with a finite
lifetime has access to the local observable algebra associated to a finite
spacetime region called a "diamond". The flow defined by the Minkowski vacuum
of a (four dimensional, conformally invariant) quantum field theory over this
algebra is also proportional to a flow in spacetime. The associated temperature
generalizes the Unruh temperature to finite lifetime observers.
Furthermore, this temperature does not vanish even in the limit in which the
acceleration is zero. The temperature associated to an inertial observer with
lifetime T, which we denote as "diamond's temperature", is 2hbar/(pi k_b
T).This temperature is related to the fact that a finite lifetime observer does
not have access to all the degrees of freedom of the quantum field theory.Comment: One reference correcte
Compilation of extended recursion in call-by-value functional languages
This paper formalizes and proves correct a compilation scheme for
mutually-recursive definitions in call-by-value functional languages. This
scheme supports a wider range of recursive definitions than previous methods.
We formalize our technique as a translation scheme to a lambda-calculus
featuring in-place update of memory blocks, and prove the translation to be
correct.Comment: 62 pages, uses pi
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