15,665 research outputs found
The inclusion process: duality and correlation inequalities
We prove a comparison inequality between a system of independent random
walkers and a system of random walkers which either interact by attracting each
other -- a process which we call here the symmetric inclusion process (SIP) --
or repel each other -- a generalized version of the well-known symmetric
exclusion process. As an application, new correlation inequalities are obtained
for the SIP, as well as for some interacting diffusions which are used as
models of heat conduction, -- the so-called Brownian momentum process, and the
Brownian energy process. These inequalities are counterparts of the
inequalities (in the opposite direction) for the symmetric exclusion process,
showing that the SIP is a natural bosonic analogue of the symmetric exclusion
process, which is fermionic. Finally, we consider a boundary driven version of
the SIP for which we prove duality and then obtain correlation inequalities.Comment: This is a new version: correlation inequalities for the Brownian
energy process are added, and the part of the asymmetric inclusion process is
removed
Novel symmetries in N = 2 supersymmetric quantum mechanical models
We demonstrate the existence of a novel set of discrete symmetries in the
context of N = 2 supersymmetric (SUSY) quantum mechanical model with a
potential function f(x) that is a generalization of the potential of the 1D
SUSY harmonic oscillator. We perform the same exercise for the motion of a
charged particle in the X-Y plane under the influence of a magnetic field in
the Z-direction. We derive the underlying algebra of the existing continuous
symmetry transformations (and corresponding conserved charges) and establish
its relevance to the algebraic structures of the de Rham cohomological
operators of differential geometry. We show that the discrete symmetry
transformations of our present general theories correspond to the Hodge duality
operation. Ultimately, we conjecture that any arbitrary N = 2 SUSY quantum
mechanical system can be shown to be a tractable model for the Hodge theory.Comment: LaTeX file, 23 pages, Title and Abstract changed, Text modified,
version to appear in Annals of Physic
Duality relations and exotic orders in electronic ladder systems
We discuss duality relations in correlated electronic ladder systems to
clarify mutual relations between various conventional and unconventional
phases. For the generalized two-leg Hubbard ladder, we find two exact duality
relations, and also one asymptotic relation which holds in the low-energy
regime. These duality relations show that unconventional (exotic) density-wave
orders such as staggered flux or circulating spin-current are directly mapped
to conventional density-wave orders, which establishes the appearance of
various exotic states with time-reversal and/or spin symmetry breaking. We also
study duality relations in the SO(5) symmetry that was proposed to unify
antiferromagnetism and d-wave superconductivity. We show that the same SO(5)
symmetry also unifies circulating spin current order and s-wave
superconductivity.Comment: 9 pages, 2 figures; Proceedings of SPQS2004 (Sendai
The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with
toroidal boundary conditions and an even number of sites provide a projection
mechanism yielding the spectra of models with a central charge c<1 including
the unitary and non-unitary minimal series. Taking into account the
half-integer angular momentum sectors - which correspond to chains with an odd
number of sites - in many cases leads to new spinor operators appearing in the
projected systems. These new sectors in the XXZ chain correspond to a new type
of frustration lines in the projected minimal models. The corresponding new
boundary conditions in the Hamiltonian limit are investigated for the Ising
model and the 3-state Potts model and are shown to be related to duality
transformations which are an additional symmetry at their self-dual critical
point. By different ways of projecting systems we find models with the same
central charge sharing the same operator content and modular invariant
partition function which however differ in the distribution of operators into
sectors and hence in the physical meaning of the operators involved. Related to
the projection mechanism in the continuum there are remarkable symmetry
properties of the finite XXZ chain. The observed degeneracies in the energy and
momentum spectra are shown to be the consequence of intertwining relations
involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published
back in 1993. It has been made available here because there has been recent
interest in conformal twisted boundary conditions. The "duality-twisted"
boundary conditions discussed in this paper are particular examples of such
boundary conditions for quantum spin chains, so there might be some renewed
interest in these result
Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
The Sachdev-Ye-Kitaev model is a -dimensional model describing
Majorana fermions or complex fermions with random interactions. This model has
various interesting properties such as approximate local criticality (power law
correlation in time), zero temperature entropy, and quantum chaos. In this
article, we propose a higher dimensional generalization of the
Sachdev-Ye-Kitaev model, which is a lattice model with Majorana fermions at
each site and random interactions between them. Our model can be defined on
arbitrary lattices in arbitrary spatial dimensions. In the large limit, the
higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev
model such as local criticality in two-point functions, zero temperature
entropy and chaos measured by the out-of-time-ordered correlation functions. In
addition, we obtain new properties unique to higher dimensions such as
diffusive energy transport and a "butterfly velocity" describing the
propagation of chaos in space. We mainly present results for a
-dimensional example, and discuss the general case near the end.Comment: 1+37 pages, published versio
- …