87 research outputs found
Random matrix analysis of the QCD sign problem for general topology
Motivated by the important role played by the phase of the fermion
determinant in the investigation of the sign problem in lattice QCD at nonzero
baryon density, we derive an analytical formula for the average phase factor of
the fermion determinant for general topology in the microscopic limit of chiral
random matrix theory at nonzero chemical potential, for both the quenched and
the unquenched case. The formula is a nontrivial extension of the expression
for zero topology derived earlier by Splittorff and Verbaarschot. Our
analytical predictions are verified by detailed numerical random matrix
simulations of the quenched theory.Comment: 33 pages, 9 figures; v2: minor corrections, references added, figures
with increased statistics, as published in JHE
Direct Instantons in QCD Nucleon Sum Rules
We study the role of direct (i.e. small-scale) instantons in QCD correlation
functions for the nucleon. They generate sizeable, nonperturbative corrections
to the conventional operator product expansion, which improve the quality of
both QCD nucleon sum rules and cure the long-standing stability problem, in
particular, of the chirally odd sum-rule.Comment: 10 pages, UMD PP#93-17
Wave packet revivals and the energy eigenvalue spectrum of the quantum pendulum
The rigid pendulum, both as a classical and as a quantum problem, is an
interesting system as it has the exactly soluble harmonic oscillator and the
rigid rotor systems as limiting cases in the low- and high-energy limits
respectively. The energy variation of the classical periodicity () is
also dramatic, having the special limiting case of at the
'top' of the classical motion (i.e. the separatrix.) We study the
time-dependence of the quantum pendulum problem, focusing on the behavior of
both the (approximate) classical periodicity and especially the quantum revival
and superrevival times, as encoded in the energy eigenvalue spectrum of the
system. We provide approximate expressions for the energy eigenvalues in both
the small and large quantum number limits, up to 4th order in perturbation
theory, comparing these to existing handbook expansions for the characteristic
values of the related Mathieu equation, obtained by other methods. We then use
these approximations to probe the classical periodicity, as well as to extract
information on the quantum revival and superrevival times. We find that while
both the classical and quantum periodicities increase monotonically as one
approaches the 'top' in energy, from either above or below, the revival times
decrease from their low- and high-energy values until very near the separatrix
where they increase to a large, but finite value.Comment: 27 pages, 8 embedded .eps figures; to appear, Annals of Physic
Zero modes, beta functions and IR/UV interplay in higher-loop QED
We analyze the relation between the short-distance behavior of quantum field
theory and the strong-field limit of the background field formalism, for QED
effective Lagrangians in self-dual backgrounds, at both one and two loop. The
self-duality of the background leads to zero modes in the case of spinor QED,
and these zero modes must be taken into account before comparing the
perturbative beta function coefficients and the coefficients of the
strong-field limit of the effective Lagrangian. At one-loop this is familiar
from instanton physics, but we find that at two-loop the role of the zero
modes, and the interplay between IR and UV effects in the renormalization, is
quite different. Our analysis is motivated in part by the remarkable simplicity
of the two-loop QED effective Lagrangians for a self-dual constant background,
and we also present here a new independent derivation of these two-loop
results.Comment: 15 pages, revtex
Generalized Zeta Functions and One-loop Corrections to Quantum Kink Masses
A method for describing the quantum kink states in the semi-classical limit
of several (1+1)-dimensional field theoretical models is developed. We use the
generalized zeta function regularization method to compute the one-loop quantum
correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon
models and another two systems with polynomial
self-interactions.Comment: 29 pages, 4 figures; version to appear in Nucl. Phys.
Supersymmetric Euler-Heisenberg effective action: Two-loop results
The two-loop Euler-Heisenberg-type effective action for N = 1 supersymmetric
QED is computed within the background field approach. The background vector
multiplet is chosen to obey the constraints D_\a W_\b = D_{(\a} W_{\b)} =
const, but is otherwise completely arbitrary. Technically, this calculation
proves to be much more laborious as compared with that carried out in
hep-th/0308136 for N = 2 supersymmetric QED, due to a lesser amount of
supersymmetry. Similarly to Ritus' analysis for spinor and scalar QED, the
two-loop renormalisation is carried out using proper-time cut-off
regularisation. A closed-form expression is obtained for the holomorphic sector
of the two-loop effective action, which is singled out by imposing a relaxed
super self-duality condition.Comment: 27 pages, 2 eps figures, LaTeX; V2: typos corrected, comments and
reference adde
Worldline Monte Carlo for fermion models at large N_f
Strongly-coupled fermionic systems can support a variety of low-energy
phenomena, giving rise to collective condensation, symmetry breaking and a rich
phase structure. We explore the potential of worldline Monte Carlo methods for
analyzing the effective action of fermionic systems at large flavor number N_f,
using the Gross-Neveu model as an example. Since the worldline Monte Carlo
approach does not require a discretized spacetime, fermion doubling problems
are absent, and chiral symmetry can manifestly be maintained. As a particular
advantage, fluctuations in general inhomogeneous condensates can conveniently
be dealt with analytically or numerically, while the renormalization can always
be uniquely performed analytically. We also critically examine the limitations
of a straightforward implementation of the algorithms, identifying potential
convergence problems in the presence of fermionic zero modes as well as in the
high-density region.Comment: 40 pages, 13 figure
Excited state quantum phase transitions in many-body systems
Phenomena analogous to ground state quantum phase transitions have recently
been noted to occur among states throughout the excitation spectra of certain
many-body models. These excited state phase transitions are manifested as
simultaneous singularities in the eigenvalue spectrum (including the gap or
level density), order parameters, and wave function properties. In this
article, the characteristics of excited state quantum phase transitions are
investigated. The finite-size scaling behavior is determined at the mean field
level. It is found that excited state quantum phase transitions are universal
to two-level bosonic and fermionic models with pairing interactions.Comment: LaTeX (elsart), 37 pages; to be published in Ann. Phys. (N.Y.
Analytic descriptions for transitional nuclei near the critical point
Exact solutions of the Bohr Hamiltonian with a five-dimensional square well
potential, in isolation or coupled to a fermion by the five-dimensional
spin-orbit interaction, are considered as examples of a new class of dynamical
symmetry or Bose-Fermi dynamical symmetry. The solutions provide baselines for
experimental studies of even-even [E(5)] and odd-mass [E(5|4)] nuclei near the
critical point of the spherical to deformed gamma-unstable phase transition.Comment: LaTeX (elsart), 53 pages; typographical correction to (3.15
Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
A recent conjecture regarding the average of the minimum eigenvalue of the
reduced density matrix of a random complex state is proved. In fact, the full
distribution of the minimum eigenvalue is derived exactly for both the cases of
a random real and a random complex state. Our results are relevant to the
entanglement properties of eigenvectors of the orthogonal and unitary ensembles
of random matrix theory and quantum chaotic systems. They also provide a rare
exactly solvable case for the distribution of the minimum of a set of N {\em
strongly correlated} random variables for all values of N (and not just for
large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat.
Phy
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