25,187 research outputs found
On the spectrum of S=1/2 XXX Heisenberg chain with elliptic exchange
It is found that the Hamiltonian of S=1/2 isotropic Heisenberg chain with
sites and elliptic non-nearest-neighbor exchange is diagonalized in each sector
of the Hilbert space with magnetization , , by means of
double quasiperiodic meromorphic solutions to the -particle quantum
Calogero-Moser problem on a line. The spectrum and highest-weight states are
determined by the solutions of the systems of transcendental equations of the
Bethe-ansatz type which arise as restrictions to particle pseudomomenta.Comment: 9 pages, Late
Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model
We derive traditional thermodynamic Bethe ansatz (TBA) equations for the
sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer
matrix. These TBA equations are identical to the ones from the string
hypothesis. Next we derive a new family of nonlinear integral equations (NLIE).
In particular, a subset of these NLIE forms a system of NLIE which contains
only a finite number of unknown functions. For r=1, this subset of NLIE reduces
to Takahashi's NLIE for the XXX spin chain. A relation between the traditional
TBA equations and our new NLIE is clarified. Based on our new NLIE, we also
calculate the high temperature expansion of the free energy.Comment: 24 pages, 4 figures, to appear in J. Phys. A: Math. Ge
An Unfolded Quantization for Twisted Hopf Algebras
In this talk I discuss a recently developed "Unfolded Quantization
Framework". It allows to introduce a Hamiltonian Second Quantization based on a
Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the
physical requirement of being a primitive element. The scheme can be applied to
theories deformed via a Drinfeld twist. I discuss in particular two cases: the
abelian twist deformation of a rotationally invariant nonrelativistic Quantum
Mechanics (the twist induces a standard noncommutativity) and the Jordanian
twist of the harmonic oscillator. In the latter case the twist induces a Snyder
non-commutativity for the space-coordinates, with a pseudo-Hermitian deformed
Hamiltonian. The "Unfolded Quantization Framework" unambiguously fixes the
non-additive effective interactions in the multi-particle sector of the
deformed quantum theory. The statistics of the particles is preserved even in
the presence of a deformation.Comment: 9 pages. Talk given at QTS7 (7th Int. Conf. on Quantum Theory and
Symmetries, Prague, August 2011
From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model
We propose a nonlinear integral equation (NLIE) with only one unknown
function, which gives the free energy of the integrable one dimensional
Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum
Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives
the solution of the T-system, plays an important role. In addition, we also
calculate the high temperature expansion of the specific heat and the magnetic
susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added;
typos corrected; to appear in J. Phys. A: Math. Ge
Yang-Yang thermodynamics on an atom chip
We investigate the behavior of a weakly interacting nearly one-dimensional
(1D) trapped Bose gas at finite temperature. We perform in situ measurements of
spatial density profiles and show that they are very well described by a model
based on exact solutions obtained using the Yang-Yang thermodynamic formalism,
in a regime where other, approximate theoretical approaches fail. We use
Bose-gas focusing [Shvarchuck etal., Phys. Rev. Lett. 89, 270404 (2002)] to
probe the axial momentum distribution of the gas, and find good agreement with
the in situ results.Comment: extended introduction and conclusions, and minor changes throughout;
accepted for publication in Phys. Rev. Let
Nonperturbative QED Effective Action at Finite Temperature
We advance a novel method for the finite-temperature effective action for
nonequilibrium quantum fields and find the QED effective action in
time-dependent electric fields, where charged pairs evolve out of equilibrium.
The imaginary part of the effective action consists of thermal loops of the
Fermi-Dirac or Bose-Einstein distribution for the initial thermal ensemble
weighted with factors for vacuum fluctuations. And the real part of the
effective action is determined by the mean number of produced pairs, vacuum
polarization, and thermal distribution. The mean number of produced pairs is
equal to twice the imaginary part. We explicitly find the finite-temperature
effective action in a constant electric field.Comment: RevTex4, 6pages, no figure; replaced by the version to be published
in Phys. Rev.
Strong short-range magnetic order in a frustrated FCC lattice and its possible role in the iron structural transformation
We investigate magnetic properties of a frustrated Heisenberg antiferromagnet
with a face-centered cubic (FCC) lattice and exchange interactions between the
nearest- and next-nearest neighbours, J1 and J2. In a collinear phase with the
wave vector Q = (pi,pi,pi) the equations of the self-consistent spin-wave
theory for the sublattice magnetization and the average short range order
parameter are obtained and numerically solved. The dependence of the Neel
temperature T_N on the ratio J2/J1 is obtained. It is shown, that at strong
enough frustration there is a wide temperature region above T_N with strong
short range magnetic order. Application of this result to description of
structural phase transition between alpha and gamma-phase of Fe is considered
Crystal properties of eigenstates for quantum cat maps
Using the Bargmann-Husimi representation of quantum mechanics on a torus
phase space, we study analytically eigenstates of quantized cat maps. The
linearity of these maps implies a close relationship between classically
invariant sublattices on the one hand, and the patterns (or `constellations')
of Husimi zeros of certain quantum eigenstates on the other hand. For these
states, the zero patterns are crystals on the torus. As a consequence, we can
compute explicit families of eigenstates for which the zero patterns become
uniformly distributed on the torus phase space in the limit . This
result constitutes a first rigorous example of semi-classical equidistribution
for Husimi zeros of eigenstates in quantized one-dimensional chaotic systems.Comment: 43 pages, LaTeX, including 7 eps figures Some amendments were made in
order to clarify the text, mainly in the 4 first sections. Figures are
unchanged. To be published in: Nonlinearit
First order transition from correlated electron semiconductor to ferromagnetic metal in single crystalline FeSi1-xGex
The phase diagram of FeSi1-xGex, obtained from magnetic, thermal and
transport measurements on single crystals, shows a first-order transition from
a correlated electron semiconductor to a ferromagnetic metal at a critical
concentration, x ~ 0.25. The gap of the insulating phase strongly decreases
with x. The specific heat coefficient appears to track the density of states of
a Kondo insulator. The phase diagram is consistent with a correlation induced
insulator-metal transition in conjunction with disorder on the Si/Ge ligand
site
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