6,011 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
Search for the Invisible Decay of Neutrons with KamLAND
The Kamioka Liquid scintillator Anti-Neutrino Detector is used in a search for single neutron or two-neutron intranuclear disappearance that would produce holes in the s-shell energy level of ^(12)C nuclei. Such holes could be created as a result of nucleon decay into invisible modes (inv), e.g., n→3ν or nn→2ν. The deexcitation of the corresponding daughter nucleus results in a sequence of space and time-correlated events observable in the liquid scintillator detector. We report on new limits for one- and two-neutron disappearance: τ(n→inv) > 5.8 × 10^(29) years and τ(nn→inv) > 1.4 × 10^(30) years at 90% C.L. These results represent an improvement of factors of ~3 and > 10^4 over previous experiments
Measurement of neutrino oscillation with KamLAND: Evidence of spectral distortion
We present results of a study of neutrino oscillation based on a 766 ton/year exposure of KamLAND to reactor antineutrinos. We observe 258 v_e candidate events with energies above 3.4 MeV compared to 365.2±23.7 events expected in the absence of neutrino oscillation. Accounting for 17.8±7.3 expected background events, the statistical significance for reactor v_e over bar (e) disappearance is 99.998%. The observed energy spectrum disagrees with the expected spectral shape in the absence of neutrino oscillation at 99.6% significance and prefers the distortion expected from v_e oscillation effects. A two-neutrino oscillation analysis of the KamLAND data gives Δm^2=7.9_(-0.5)^(+0.6)x10^(-5) eV^2. A global analysis of data from KamLAND and solar-neutrino experiments yields
Δm^2=7.9_(-0.5)^(+0.6)x10^(-5) eV^2 and tan^2θ=0.40_(-0.07)^(+0.10), the most precise determination to date
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
A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
The generalized second law is proven for semiclassical quantum fields falling
across a causal horizon, minimally coupled to general relativity. The proof is
much more general than previous proofs in that it permits the quantum fields to
be rapidly changing with time, and shows that entropy increases when comparing
any slice of the horizon to any earlier slice. The proof requires the existence
of an algebra of observables restricted to the horizon, satisfying certain
axioms (Determinism, Ultralocality, Local Lorentz Invariance, and Stability).
These axioms are explicitly verified in the case of free fields of various
spins, as well as 1+1 conformal field theories. The validity of the axioms for
other interacting theories is discussed.Comment: 44 pages, 1 fig. v3: clarified Sec. 2; signs, factors/notation
corrected in Eq. 75-80, 105-107; reflects published version. v4: clearer
axioms in Sec. 2.3, fixed compensating factor of 2 errors in Eq. 54,74 etc.,
and other errors. Results unaffected. v5: fixed typos. v6: replaced faulty
1+1 CFT argument, added note on recent progres
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
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
Localized Endomorphisms of the Chiral Ising Model
Based on the treatment of the chiral Ising model by Mack and Schomerus, we
present examples of localized endomorphisms and
. It is shown that they lead to the same
superselection sectors as the global ones in the sense that unitary equivalence
and holds. Araki's formalism of the selfdual CAR algebra is
used for the proof. We prove local normality and extend representations and
localized endomorphisms to a global algebra of observables which is generated
by local von Neumann algebras on the punctured circle. In this framework, we
manifestly prove fusion rules and derive statistics operators.Comment: 41 pages, latex2
The - divergence and Mixing times of quantum Markov processes
We introduce quantum versions of the -divergence, provide a detailed
analysis of their properties, and apply them in the investigation of mixing
times of quantum Markov processes. An approach similar to the one presented in
[1-3] for classical Markov chains is taken to bound the trace-distance from the
steady state of a quantum processes. A strict spectral bound to the convergence
rate can be given for time-discrete as well as for time-continuous quantum
Markov processes. Furthermore the contractive behavior of the
-divergence under the action of a completely positive map is
investigated and contrasted to the contraction of the trace norm. In this
context we analyse different versions of quantum detailed balance and, finally,
give a geometric conductance bound to the convergence rate for unital quantum
Markov processes
Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
A limitation on simultaneous measurement of two arbitrary positive operator
valued measures is discussed. In general, simultaneous measurement of two
noncommutative observables is only approximately possible. Following Werner's
formulation, we introduce a distance between observables to quantify an
accuracy of measurement. We derive an inequality that relates the achievable
accuracy with noncommutativity between two observables. As a byproduct a
necessary condition for two positive operator valued measures to be
simultaneously measurable is obtained.Comment: 7 pages, 1 figure. To appear in Phys. Rev.
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