571 research outputs found
Calculation of the Two-body T-matrix in Configuration Space
A spectral integral method (IEM) for solving the two-body Schroedinger
equation in configuration space is generalized to the calculation of the
corresponding T-matrix. It is found that the desirable features of the IEM,
such as the economy of mesh-points for a given required accuracy, are carried
over also to the solution of the T-matrix. However the algorithm is
considerably more complex, because the T-matrix is a function of two variables
r and r', rather than only one variable r, and has a slope discontinuity at
r=r'. For a simple exponential potential an accuracy of 7 significant figures
is achieved, with the number N of Chebyshev support points in each partition
equal to 17. For a potential with a large repulsive core, such as the potential
between two He atoms, the accuracy decreases to 4 significant figures, but is
restored to 7 if N is increased to 65.Comment: 22 pages, 1 table 8 figure
Acoustics of tachyon Fermi gas
We consider a Fermi gas of free tachyons as a continuous medium and find
whether it satisfies the causality condition. There is no stable tachyon matter
with the particle density below critical value and the Fermi momentum
that depends on the tachyon mass . The pressure
and energy density cannot be arbitrary small, but the situation is
not forbidden. Existence of shock waves in tachyon gas is also discussed. At
low density the tachyon matter remains stable but no shock wave
do survive.Comment: 14 pages, 2 figures (color
Shock waves in superconducting cosmic strings: growth of current
Intrinsic equations of motion of superconducting cosmic string may admit
solutions in the shock-wave form that implies discontinuity of the current term
\chi. The hypersurface of discontinuity propagates at finite velocity
determined by finite increment \Delta \chi =\chi_+ -\chi_-. The current
increases \chi_+>\chi_- in stable shocks but transition between spacelike (\chi
>0) and timelike (\chi<0) currents is impossible.Comment: 13 pages, 3 figure
Absence of Domain Wall Roughening in a Transverse Field Ising Model with Long-Range Interactions
We investigate roughening transitions in the context of transverse-field
Ising models. As a modification of the transverse Ising model with short range
interactions, which has been shown to exhibit domain wall roughening, we have
looked into the possibility of a roughening transition for the case of
long-range interactions, since such a system is physically realized in the
insulator LiHoF4. The combination of strong Ising anisotropy and long-range
forces lead naturally to the formation of domain walls but we find that the
long-range forces destroy the roughening transition.Comment: 7 pages, 5 figures, revtex
Anomalous Hydrodynamics
Our goal is to examine the role of anomalies in the hydrodynamic regime of
field theories. We employ methods based on gauge/gravity duality to examine
R-charge anomalies in the hydrodynamic regime of stronly t'Hooft coupled, large
N, N = 4 Super Yang-Mills. We use a single particle spectrum treatment based on
the familiar "level crossing" picture of chiral anomalies to investigate
thermalized, massless QED. In each case, we work in the presence of a
homogeneous background magnetic field, and find the same result. Regardless of
whether a paricular current is anomalously non-conserved or not, as long as it
participates in an anomalous 3-pt. correlator, its constitutive relation
recieves a new term, proportional to a product of the anomaly coefficient, the
magnetic field, and any charge density participating in the anomaly. This
agrees with results found by Alekseev et.al. for QED. We include a general,
symmetry based argument for the presence of such terms, and use linear response
theory to determine their coefficients in a model with anomalous global
charges. This last method we apply to briefly examine baryon transport in
chiral QCD in a strong magnetic field.Comment: 23 pages, 2 figures. To be submitted to JHE
Thermodynamic curvature measures interactions
Thermodynamic fluctuation theory originated with Einstein who inverted the
relation to express the number of states in terms of entropy:
. The theory's Gaussian approximation is discussed in most
statistical mechanics texts. I review work showing how to go beyond the
Gaussian approximation by adding covariance, conservation, and consistency.
This generalization leads to a fundamentally new object: the thermodynamic
Riemannian curvature scalar , a thermodynamic invariant. I argue that
is related to the correlation length and suggest that the sign of
corresponds to whether the interparticle interactions are effectively
attractive or repulsive.Comment: 29 pages, 7 figures (added reference 27
Discrete Symmetry and Stability in Hamiltonian Dynamics
In this tutorial we address the existence and stability of periodic and
quasiperiodic orbits in N degree of freedom Hamiltonian systems and their
connection with discrete symmetries. Of primary importance in our study are the
nonlinear normal modes (NNMs), i.e periodic solutions which represent
continuations of the system's linear normal modes in the nonlinear regime. We
examine the existence of such solutions and discuss different methods for
constructing them and studying their stability under fixed and periodic
boundary conditions. In the periodic case, we employ group theoretical concepts
to identify a special type of NNMs called one-dimensional "bushes". We describe
how to use linear combinations such NNMs to construct s(>1)-dimensional bushes
of quasiperiodic orbits, for a wide variety of Hamiltonian systems and exploit
the symmetries of the linearized equations to simplify the study of their
destabilization. Applying this theory to the Fermi Pasta Ulam (FPU) chain, we
review a number of interesting results, which have appeared in the recent
literature. We then turn to an analytical and numerical construction of
quasiperiodic orbits, which does not depend on the symmetries or boundary
conditions. We demonstrate that the well-known "paradox" of FPU recurrences may
be explained in terms of the exponential localization of the energies Eq of
NNM's excited at the low part of the frequency spectrum, i.e. q=1,2,3,....
Thus, we show that the stability of these low-dimensional manifolds called
q-tori is related to the persistence or FPU recurrences at low energies.
Finally, we discuss a novel approach to the stability of orbits of conservative
systems, the GALIk, k=2,...,2N, by means of which one can determine accurately
and efficiently the destabilization of q-tori, leading to the breakdown of
recurrences and the equipartition of energy, at high values of the total energy
E.Comment: 50 pages, 13 figure
Bulk Viscosity, Decaying Dark Matter, and the Cosmic Acceleration
We discuss a cosmology in which cold dark-matter particles decay into
relativistic particles. We argue that such decays could lead naturally to a
bulk viscosity in the cosmic fluid. For decay lifetimes comparable to the
present hubble age, this bulk viscosity enters the cosmic energy equation as an
effective negative pressure. We investigate whether this negative pressure is
of sufficient magnitude to account fo the observed cosmic acceleration. We show
that a single decaying species in a flat, dark-matter dominated cosmology
without a cosmological constant cannot reproduce the observed
magnitude-redshift relation from Type Ia supernovae. However, a delayed bulk
viscosity, possibly due to a cascade of decaying particles may be able to
account for a significant fraction of the apparent cosmic acceleration.
Possible candidate nonrelativistic particles for this scenario include sterile
neutrinos or gauge-mediated decaying supersymmetric particles.Comment: 7 pages, 4 figure
Heat exchange mediated by a quantum system
We consider heat transfer between two thermal reservoirs mediated by a
quantum system using the generalized quantum Langevin equation. The thermal
reservoirs are treated as ensembles of oscillators within the framework of the
Drude-Ullersma model. General expressions for the heat current and thermal
conductance are obtained for arbitrary coupling strength between the reservoirs
and the mediator and for different temperature regimes. As an application of
these results we discuss the origin of Fourier's law in a chain of large, but
finite subsystems coupled to each other by the quantum mediators. We also
address a question of anomalously large heat current between the STM tip and
substrate found in a recent experiment. The question of minimum thermal
conductivity is revisited in the framework of scaling theory as a potential
application of the developed approach.Comment: 16 pages, 6 figure
Light masses in short distance penguin loops
Penguin diagrams for decays such as involve virtual loops
of or other light quarks. Logarithms of the virtual quark mass could, in
principle, influence the phenomenological analysis of the decay. It is thus
important to study these logarithms to all orders in QCD perturbation theory.
In this paper we show that, at arbitrary order, the matrix elements of
operators in the effective hamiltonian contributing to are
finite for the limit of in penguin loops.Comment: 11 pages, 6 ps figures. Revise
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