647 research outputs found

### Analysis of the exactness of mean-field theory in long-range interacting systems

Relationships between general long-range interacting classical systems on a
lattice and the corresponding mean-field models (infinitely long-range
interacting models) are investigated. We study systems in arbitrary dimension d
for periodic boundary conditions and focus on the free energy for fixed value
of the total magnetization. As a result, it is shown that the equilibrium free
energy of the long-range interacting systems are exactly the same as that of
the corresponding mean-field models (exactness of the mean-field theory).
Moreover, the mean-field metastable states can be also preserved in general
long-range interacting systems. It is found that in the case that the
magnetization is conserved, the mean-field theory does not give correct
property in some parameter region.Comment: 4 pages, 5 figures; clarifications and discussion about boundary
effects is added; the title is change

### Noncommutative Manifolds from the Higgs Sector of Coincident D-Branes

The Higgs sector of the low-energy physics of n of coincident D-branes
contains the necessary elements for constructing noncommutative manifolds. The
coordinates orthogonal to the coincident branes, as well as their conjugate
momenta, take values in the Lie algebra of the gauge group living inside the
brane stack. In the limit when n=\infty (and in the absence of orientifolds),
this is the unitary Lie algebra u(\infty). Placing a smooth manifold K
orthogonally to the stack of coincident D-branes one can construct a
noncommutative C*-algebra that provides a natural definition of a
noncommutative partner for the manifold K.Comment: 10 page

### Validity and failure of some entropy inequalities for CAR systems

Basic properties of von Neumann entropy such as the triangle inequality and
what we call MONO-SSA are studied for CAR systems.
We show that both inequalities hold for any even state. We construct a
certain class of noneven states giving counter examples of those inequalities.
It is not always possible to extend a set of prepared states on disjoint
regions to some joint state on the whole region for CAR systems.
However, for every even state, we have its `symmetric purification' by which
the validity of those inequalities is shown.
Some (realized) noneven states have peculiar state correlations among
subsystems and induce the failure of those inequalities.Comment: 14 pages, latex, to appear in JMP. Some typos are correcte

### Statistics and Quantum Chaos

We use multi-time correlation functions of quantum systems to construct
random variables with statistical properties that reflect the degree of
complexity of the underlying quantum dynamics.Comment: 12 pages, LateX, no figures, restructured versio

### Celestial mechanics in Kerr spacetime

The dynamical parameters conventionally used to specify the orbit of a test
particle in Kerr spacetime are the energy $E$, the axial component of the
angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are
obtained by solving the Hamilton-Jacobi equation for the dynamical problem of
geodesic motion. Employing the action-angle variable formalism, on the other
hand, yields a different set of constants of motion, namely, the fundamental
frequencies $\omega_{r}$, $\omega_{\theta}$ and $\omega_{\phi}$ associated with
the radial, polar and azimuthal components of orbital motion. These
frequencies, naturally, determine the time scales of orbital motion and,
furthermore, the instantaneous gravitational wave spectrum in the adiabatic
approximation. In this article, it is shown that the fundamental frequencies
are geometric invariants and explicit formulas in terms of quadratures are
derived. The numerical evaluation of these formulas in the case of a rapidly
rotating black hole illustrates the behaviour of the fundamental frequencies as
orbital parameters such as the semi-latus rectum $p$, the eccentricity $e$ or
the inclination parameter $\theta_{-}$ are varied. The limiting cases of
circular, equatorial and Keplerian motion are investigated as well and it is
shown that known results are recovered from the general formulas.Comment: 25 pages (LaTeX), 5 figures, submitted to Class. Quantum Gra

### Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors

One of the defining properties of the conventional three-dimensional
("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its
characteristic magnetoelectric effect, as described by axion electrodynamics.
In this paper, we discuss an analogue of such a magnetoelectric effect in the
thermal (or gravitational) and the magnetic dipole responses in all symmetry
classes which admit topologically non-trivial insulators or superconductors to
exist in three dimensions. In particular, for topological superconductors (or
superfluids) with time-reversal symmetry which lack SU(2) spin rotation
symmetry (e.g. due to spin-orbit interactions), such as the B phase of $^3$He,
the thermal response is the only probe which can detect the non-trivial
topological character through transport. We show that, for such topological
superconductors, applying a temperature gradient produces a thermal- (or mass-)
surface current perpendicular to the thermal gradient. Such charge, thermal, or
magnetic dipole responses provide a definition of topological insulators and
superconductors beyond the single-particle picture. Moreover we find, for a
significant part of the 'ten-fold' list of topological insulators found in
previous work in the absence of interactions, that in general dimensions the
effective field theory describing the space-time responses is governed by a
field theory anomaly. Since anomalies are known to be insensitive to whether
the underlying fermions are interacting or not, this shows that the
classification of these topological insulators is robust to adiabatic
deformations by interparticle interactions in general dimensionality. In
particular, this applies to symmetry classes DIII, CI, and AIII in three
spatial dimensions, and to symmetry classes D and C in two spatial dimensions.Comment: 16 pages, 2 figure

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