728 research outputs found
Entropy and Correlation Functions of a Driven Quantum Spin Chain
We present an exact solution for a quantum spin chain driven through its
critical points. Our approach is based on a many-body generalization of the
Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The
resulting nonequilibrium state of the system, while being a pure quantum state,
has local properties of a mixed state characterized by finite entropy density
associated with Kibble-Zurek defects. The entropy, as well as the finite spin
correlation length, are functions of the rate of sweep through the critical
point. We analyze the anisotropic XY spin 1/2 model evolved with a full
many-body evolution operator. With the help of Toeplitz determinants calculus,
we obtain an exact form of correlation functions. The properties of the evolved
system undergo an abrupt change at a certain critical sweep rate, signaling
formation of ordered domains. We link this phenomenon to the behavior of
complex singularities of the Toeplitz generating function.Comment: 16 pgs, 7 fg
Zeros of the Jimbo, Miwa, Ueno tau function
We introduce a family of local deformations for meromorphic connections on
the Riemann sphere in the neighborhood of a higher rank (simple) singularity.
Following a scheme introduced by Malgrange we use these local models to prove
that the zeros of the tau function introduced by Jimbo, Miwa and Ueno occur
precisely at those points in the deformation space at which a certain
Birkhoff-Riemann- Hilbert problem fails to have a solution.Comment: 59 page
Long-time asymptotics of the nonlinear SchrÖdinger equation shock problem
The long-time asymptotics of two colliding plane waves governed by the focusing nonlinear SchrÖdinger equation are analyzed via the inverse scattering method. We find three asymptotic regions in space-time: a region with the original wave modified by a phase perturbation, a residual region with a one-phase wave, and an intermediate transition region with a modulated two-phase wave. The leading-order terms for the three regions are computed with error estimates using the steepest-descent method for Riemann-Hilbert problems. The nondecaying initial data requires a new adaptation of this method. A new breaking mechanism involving a complex conjugate pair of branch points emerging from the real axis is observed between the residual and transition regions. Also, the effect of the collision is felt in the plane-wave state well beyond the shock front at large times. © 2007 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/56049/1/20179_ftp.pd
Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions
We analyze behavior of correlated electrons described by Hubbard-like models
at intermediate and strong coupling. We show that with increasing interaction a
pole in a generic two-particle Green function is approached. The pole signals
metal-insulator transition at half filling and gives rise to a new vanishing
``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To
describe the critical behavior at the metal-insulator transition a novel,
self-consistent diagrammatic technique with two-particle Green functions is
developed. The theory is based on the linked-cluster expansion for the
thermodynamic potential with electron-electron interaction as propagator.
Parquet diagrams with a generating functional are derived. Numerical
instabilities due to the metal-insulator transition are demonstrated on
simplifications of the parquet algebra with ring and ladder series only. A
stable numerical solution in the critical region is reached by factorization of
singular terms via a low-frequency expansion in the vertex function. We stress
the necessity for dynamical vertex renormalizations, missing in the simple
approximations, in order to describe the critical, strong-coupling behavior
correctly. We propose a simplification of the full parquet approximation by
keeping only most divergent terms in the asymptotic strong-coupling region. A
qualitatively new, feasible approximation suitable for the description of a
transition from weak to strong coupling is obtained.Comment: 17 pages, 4 figures, REVTe
Electroproduction of tensor mesons in QCD
Due to multiple possible polarizations hard exclusive production of tensor
mesons by virtual photons or in heavy meson decays offers interesting
possibilities to study the helicity structure of the underlying short-distance
process. Motivated by the first measurement of the transition form factor
at large momentum transfers by the BELLE
collaboration we present an improved QCD analysis of this reaction in the
framework of collinear factorization including contributions of twist-three
quark-antiquark-gluon operators and an estimate of soft end-point corrections
using light-cone sum rules. The results appear to be in a very good agreement
with the data, in particular the predicted scaling behavior is reproduced in
all cases.Comment: 27 pages, 5 figure
Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra
We derive the long-time asymptotics for the Toda shock problem using the
nonlinear steepest descent analysis for oscillatory Riemann--Hilbert
factorization problems. We show that the half plane of space/time variables
splits into five main regions: The two regions far outside where the solution
is close to free backgrounds. The middle region, where the solution can be
asymptotically described by a two band solution, and two regions separating
them, where the solution is asymptotically given by a slowly modulated two band
solution. In particular, the form of this solution in the separating regions
verifies a conjecture from Venakides, Deift, and Oba from 1991.Comment: 39 page
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