3,000 research outputs found
When is the deconfinement phase transition universal?
Pure Yang-Mills theory has a finite-temperature phase transition, separating
the confined and deconfined bulk phases. Svetitsky and Yaffe conjectured that
if this phase transition is of second order, it belongs to the universality
class of transitions for particular scalar field theories in one lower
dimension. We examine Yang-Mills theory with the symplectic gauge groups Sp(N).
We find new evidence supporting the Svetitsky-Yaffe conjecture and make our own
conjecture as to which gauge theories have a universal second order
deconfinement phase transition.Comment: 5 pages, 4 figures; Contribution to Confinement 2003, Tokyo, Japan,
July 21-24, 200
Self-adjoint Extensions for Confined Electrons:from a Particle in a Spherical Cavity to the Hydrogen Atom in a Sphere and on a Cone
In a recent study of the self-adjoint extensions of the Hamiltonian of a
particle confined to a finite region of space, in which we generalized the
Heisenberg uncertainty relation to a finite volume, we encountered bound states
localized at the wall of the cavity. In this paper, we study this situation in
detail both for a free particle and for a hydrogen atom centered in a spherical
cavity. For appropriate values of the self-adjoint extension parameter, the
bound states lo calized at the wall resonate with the standard hydrogen bound
states. We also examine the accidental symmetry generated by the Runge-Lenz
vector, which is explicitly broken in a spherical cavity with general Robin
boundary conditions. However, for specific radii of the confining sphere, a
remnant of the accidental symmetry persists. The same is true for an electron
moving on the surface of a finite circular cone, bound to its tip by a 1/r
potential.Comment: 22 pages, 9 Figure
Monte Carlo Study of Correlations in Quantum Spin Chains at Non-Zero Temperature
Antiferromagnetic Heisenberg spin chains with various spin values
() are studied numerically with the quantum Monte Carlo
method. Effective spin chains are realized by ferromagnetically coupling
antiferromagnetic spin chains with . The temperature dependence
of the uniform susceptibility, the staggered susceptibility, and the static
structure factor peak intensity are computed down to very low temperatures,
. The correlation length at each temperature is deduced from
numerical measurements of the instantaneous spin-spin correlation function. At
high temperatures, very good agreement with exact results for the classical
spin chain is obtained independent of the value of . For =2 chains which
have a gap , the correlation length and the uniform susceptibility in
the temperature range are well predicted by a semi-classical
theory due to Damle and Sachdev.Comment: LaTeX EPJ macr
Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements
We consider a large quantum system with spins whose dynamics is
driven entirely by measurements of the total spin of spin pairs. This gives
rise to a dissipative coupling to the environment. When one averages over the
measurement results, the corresponding real-time path integral does not suffer
from a sign problem. Using an efficient cluster algorithm, we study the
real-time evolution of a 2-d Heisenberg antiferromagnet, which is driven to a
disordered phase, either by sporadic measurements or by continuous monitoring
described by Lindblad evolution.Comment: 5 pages, 7 figure
Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the -Function Potential in 1-dimensional Relativistic Quantum Mechanics
We consider the Schr\"odinger equation for a relativistic point particle in
an external 1-dimensional -function potential. Using dimensional
regularization, we investigate both bound and scattering states, and we obtain
results that are consistent with the abstract mathematical theory of
self-adjoint extensions of the pseudo-differential operator . Interestingly, this relatively simple system is asymptotically free. In
the massless limit, it undergoes dimensional transmutation and it possesses an
infra-red conformal fixed point. Thus it can be used to illustrate non-trivial
concepts of quantum field theory in the simpler framework of relativistic
quantum mechanics
Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity
The non-relativistic hydrogen atom enjoys an accidental symmetry,
that enlarges the rotational symmetry, by extending the angular
momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom
the accidental symmetry is partially lifted. Due to the Johnson-Lippmann
operator, which commutes with the Dirac Hamiltonian, some degeneracy remains.
When the non-relativistic hydrogen atom is put in a spherical cavity of radius
with perfectly reflecting Robin boundary conditions, characterized by a
self-adjoint extension parameter , in general the accidental
symmetry is lifted. However, for (where is the Bohr
radius and is the orbital angular momentum) some degeneracy remains when
or . In the relativistic case, we
consider the most general spherically and parity invariant boundary condition,
which is characterized by a self-adjoint extension parameter. In this case, the
remnant accidental symmetry is always lifted in a finite volume. We also
investigate the accidental symmetry in the context of the Pauli equation, which
sheds light on the proper non-relativistic treatment including spin. In that
case, again some degeneracy remains for specific values of and .Comment: 27 pages, 7 figure
Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD
The order parameter of a finite system with a spontaneously broken continuous
global symmetry acts as a quantum mechanical rotor. Both antiferromagnets with
a spontaneously broken spin symmetry and massless QCD with a broken
chiral symmetry have rotor spectra when considered in
a finite volume. When an electron or hole is doped into an antiferromagnet or
when a nucleon is propagating through the QCD vacuum, a Berry phase arises from
a monopole field and the angular momentum of the rotor is quantized in
half-integer units.Comment: 4 page
Majorana Fermions in a Box
Majorana fermion dynamics may arise at the edge of Kitaev wires or
superconductors. Alternatively, it can be engineered by using trapped ions or
ultracold atoms in an optical lattice as quantum simulators. This motivates the
theoretical study of Majorana fermions confined to a finite volume, whose
boundary conditions are characterized by self-adjoint extension parameters.
While the boundary conditions for Dirac fermions in -d are characterized
by a 1-parameter family, , of self-adjoint extensions,
for Majorana fermions is restricted to . Based on this result,
we compute the frequency spectrum of Majorana fermions confined to a 1-d
interval. The boundary conditions for Dirac fermions confined to a 3-d region
of space are characterized by a 4-parameter family of self-adjoint extensions,
which is reduced to two distinct 1-parameter families for Majorana fermions. We
also consider the problems related to the quantum mechanical interpretation of
the Majorana equation as a single-particle equation. Furthermore, the equation
is related to a relativistic Schr\"odinger equation that does not suffer from
these problems.Comment: 23 pages, 2 figure
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