2,251 research outputs found
Equilibrium Statistical Mechanics of Fermion Lattice Systems
We study equilibrium statistical mechanics of Fermion lattice systems which
require a different treatment compared with spin lattice systems due to the
non-commutativity of local algebras for disjoint regions.
Our major result is the equivalence of the KMS condition and the variational
principle with a minimal assumption for the dynamics and without any explicit
assumption on the potential. It holds also for spin lattice systems as well,
yielding a vast improvement over known results.
All formulations are in terms of a C*-dynamical systems for the Fermion (CAR)
algebra with all or a part of the following assumptions:
(I) The interaction is even with respect to the Fermion number.
(Automatically satisfied when (IV) below is assumed.)
(II) All strictly local elements of the algebra have the first time
derivative.
(III) The time derivatives in (II) determine the dynamics.
(IV) The interaction is lattice translation invariant.
A major technical tool is the conditional expectation from the total algebra
onto the local subalgebra for any finite subset of the lattice, which induces a
system of commuting squares. This technique overcomes the lack of tensor
product structures for Fermion systems and even simplifies many known arguments
for spin lattice systems.Comment: 103 pages, no figure. The Section 13 has become simpler and a problem
in 14.1 is settled thanks to a referee. The format has been revised according
to the suggestion of this and the other referee
Out of equilibrium correlations in the XY chain
We study the transversal XY spin-spin correlations in the non-equilibrium
steady state constructed in \cite{AP03} and prove their spatial exponential
decay close to equilibrium
Universal fermionization of bosons on permutative representations of the Cuntz algebra
Bosons and fermions are described by using canonical generators of Cuntz
algebras on any permutative representation. We show a fermionization of bosons
which universally holds on any permutative representation of the Cuntz algebra
. As examples, we show fermionizations on the Fock space and the
infinite wedge.Comment: 12 page
Non-anticommutative chiral singlet deformation of N=(1,1) gauge theory
We study the SO(4)x SU(2) invariant Q-deformation of Euclidean N=(1,1) gauge
theories in the harmonic superspace formulation. This deformation preserves
chirality and Grassmann harmonic analyticity but breaks N=(1,1) to N=(1,0)
supersymmetry. The action of the deformed gauge theory is an integral over the
chiral superspace, and only the purely chiral part of the covariant superfield
strength contributes to it. We give the component form of the N=(1,0)
supersymmetric action for the gauge groups U(1) and U(n>1). In the U(1) and
U(2) cases, we find the explicit nonlinear field redefinition (Seiberg-Witten
map) relating the deformed N=(1,1) gauge multiplet to the undeformed one. This
map exists in the general U(n) case as well, and we use this fact to argue that
the deformed U(n) gauge theory can be nonlinearly reduced to a theory with the
gauge group SU(n).Comment: 1+25 pages; v2: corrected eqs.(2.7),(3.12),(4.31-33) and typos; v3:
corrected eqs.(3.29),(4.7),(A.5),(A.21), ref. added, published versio
Particle Redistribution During Dendritic Solidification of Particle Suspensions
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65783/1/j.1551-2916.2006.01094.x.pd
The H\"older Inequality for KMS States
We prove a H\"older inequality for KMS States, which generalises a well-known
trace-inequality. Our results are based on the theory of non-commutative
-spaces.Comment: 10 page
Quantizing the damped harmonic oscillator
We consider the Fermi quantization of the classical damped harmonic
oscillator (dho). In past work on the subject, authors double the phase space
of the dho in order to close the system at each moment in time. For an
infinite-dimensional phase space, this method requires one to construct a
representation of the CAR algebra for each time. We show that unitary dilation
of the contraction semigroup governing the dynamics of the system is a logical
extension of the doubling procedure, and it allows one to avoid the
mathematical difficulties encountered with the previous method.Comment: 4 pages, no figure
Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model
We investigate the quantum aspects of a charged hypermultiplet in deformed
N=(1,1) superspace with singlet non-anticommutative deformation of
supersymmetry. This model is a "star" modification of the hypermultiplet
interacting with a background Abelian vector superfield. We prove that this
model is renormalizable in the sense that the divergent part of the effective
action is proportional to the N=(1,0) non-anticommutative super Yang-Mills
action. We also calculate the finite part of the low-energy effective action
depending on the vector multiplet, which corresponds to the (anti)holomorphic
potential. The holomorphic piece is just deformed to the star-generalization of
the standard holomorphic potential, while the antiholomorphic piece is not. We
also reveal the component structure and find the deformation of the mass and
the central charge.Comment: 22 pages, 1 figur
Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM Construction
We study an extension of the ADHM construction to give deformed
anti-self-dual (ASD) instantons in N=1/2 super Yang-Mills theory with U(n)
gauge group. First we extend the exterior algebra on superspace to
non(anti)commutative superspace and show that the N=1/2 super Yang-Mills theory
can be reformulated in a geometrical way. By using this exterior algebra, we
formulate a non(anti)commutative version of the super ADHM construction and
show that the curvature two-form superfields obtained by our construction do
satisfy the deformed ASD equations and thus we establish the deformed super
ADHM construction. We also show that the known deformed U(2) one instanton
solution is obtained by this construction.Comment: 32 pages, LaTeX, v2: typos corrected, references adde
Kakutani Dichotomy on Free States
Two quasi-free states on a CAR or CCR algebra are shown to generate
quasi-equivalent representations unless they are disjoint.Comment: 12 page
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