282 research outputs found
Peierls Distortion and Quantum Solitons
Peierls distortion and quantum solitons are two hallmarks of 1-dimensional
condensed-matter systems. Here we propose a quantum model for a one-dimensional
system of non-linearly interacting electrons and phonons, where the phonons are
represented via coherent states. This model permits a unified description of
Peierls distortion and quantum solitons. The non-linear electron-phonon
interaction and the resulting deformed symmetry of the Hamiltonian are
distinctive features of the model, of which that of Su, Schrieffer and Heeger
can be regarded as a special case
Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model
We investigate the potential energy surface of a phi^4 model with infinite
range interactions. All stationary points can be uniquely characterized by
three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_-
= 1, provided that the interaction strength mu is smaller than a critical
value. The saddle index n_s is equal to alpha_0 and its distribution function
has a maximum at n_s^max = 1/3. The density p(e) of stationary points with
energy per particle e, as well as the Euler characteristic chi(e), are singular
at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu)
\neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per
particle at the thermodynamic phase transition point T_c. This proves that
previous claims that the topological and thermodynamic transition points
coincide is not valid, in general. Both types of singularities disappear for H
\neq 0. The average saddle index bar{n}_s as function of e decreases
monotonically with e and vanishes at the ground state energy, only. In
contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is
given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 >
upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure
Isentropic Curves at Magnetic Phase Transitions
Experiments on cold atom systems in which a lattice potential is ramped up on
a confined cloud have raised intriguing questions about how the temperature
varies along isentropic curves, and how these curves intersect features in the
phase diagram. In this paper, we study the isentropic curves of two models of
magnetic phase transitions- the classical Blume-Capel Model (BCM) and the Fermi
Hubbard Model (FHM). Both Mean Field Theory (MFT) and Monte Carlo (MC) methods
are used. The isentropic curves of the BCM generally run parallel to the phase
boundary in the Ising regime of low vacancy density, but intersect the phase
boundary when the magnetic transition is mainly driven by a proliferation of
vacancies. Adiabatic heating occurs in moving away from the phase boundary. The
isentropes of the half-filled FHM have a relatively simple structure, running
parallel to the temperature axis in the paramagnetic phase, and then curving
upwards as the antiferromagnetic transition occurs. However, in the doped case,
where two magnetic phase boundaries are crossed, the isentrope topology is
considerably more complex
Bose-Einstein condensation in inhomogeneous Josephson arrays
We show that spatial Bose-Einstein condensation of non-interacting bosons
occurs in dimension d < 2 over discrete structures with inhomogeneous topology
and with no need of external confining potentials. Josephson junction arrays
provide a physical realization of this mechanism. The topological origin of the
phenomenon may open the way to the engineering of quantum devices based on
Bose-Einstein condensation. The comb array, which embodies all the relevant
features of this effect, is studied in detail.Comment: 4 pages, 5 figure
Quantum geometry and quantum algorithms
Motivated by algorithmic problems arising in quantum field theories whose
dynamical variables are geometric in nature, we provide a quantum algorithm
that efficiently approximates the colored Jones polynomial. The construction is
based on the complete solution of Chern-Simons topological quantum field theory
and its connection to Wess-Zumino-Witten conformal field theory. The colored
Jones polynomial is expressed as the expectation value of the evolution of the
q-deformed spin-network quantum automaton. A quantum circuit is constructed
capable of simulating the automaton and hence of computing such expectation
value. The latter is efficiently approximated using a standard sampling
procedure in quantum computation.Comment: Submitted to J. Phys. A: Math-Gen, for the special issue ``The
Quantum Universe'' in honor of G. C. Ghirard
Bose-Einstein Condensation on inhomogeneous complex networks
The thermodynamic properties of non interacting bosons on a complex network
can be strongly affected by topological inhomogeneities. The latter give rise
to anomalies in the density of states that can induce Bose-Einstein
condensation in low dimensional systems also in absence of external confining
potentials. The anomalies consist in energy regions composed of an infinite
number of states with vanishing weight in the thermodynamic limit. We present a
rigorous result providing the general conditions for the occurrence of
Bose-Einstein condensation on complex networks in presence of anomalous
spectral regions in the density of states. We present results on spectral
properties for a wide class of graphs where the theorem applies. We study in
detail an explicit geometrical realization, the comb lattice, which embodies
all the relevant features of this effect and which can be experimentally
implemented as an array of Josephson Junctions.Comment: 11 pages, 9 figure
Thermalization of a Brownian particle via coupling to low-dimensional chaos
It is shown that a paradigm of classical statistical mechanics --- the
thermalization of a Brownian particle --- has a low-dimensional, deterministic
analogue: when a heavy, slow system is coupled to fast deterministic chaos, the
resultant forces drive the slow degrees of freedom toward a state of
statistical equilibrium with the fast degrees. This illustrates how concepts
useful in statistical mechanics may apply in situations where low-dimensional
chaos exists.Comment: Revtex, 11 pages, no figures
A Topological String: The Rasetti-Regge Lagrangian, Topological Quantum Field Theory, and Vortices in Quantum Fluids
The kinetic part of the Rasetti-Regge action I_{RR} for vortex lines is
studied and links to string theory are made. It is shown that both I_{RR} and
the Polyakov string action I_{Pol} can be constructed with the same field X^mu.
Unlike I_{NG}, however, I_{RR} describes a Schwarz-type topological quantum
field theory. Using generators of classical Lie algebras, I_{RR} is generalized
to higher dimensions. In all dimensions, the momentum 1-form P constructed from
the canonical momentum for the vortex belongs to the first cohomology class
H^1(M,R^m) of the worldsheet M swept-out by the vortex line. The dynamics of
the vortex line thus depend directly on the topology of M. For a vortex ring,
the equations of motion reduce to the Serret-Frenet equations in R^3, and in
higher dimensions they reduce to the Maurer-Cartan equations for so(m).Comment: To appear in Journal of Physics
Quantum global vortex strings in a background field
We consider quantum global vortex string correlation functions, within the
Kalb-Ramond framework, in the presence of a background field-strength tensor
and investigate the conditions under which this yields a nontrivial
contribution to those correlation functions. We show that a background field
must be supplemented to the Kalb-Ramond theory, in order to correctly describe
the quantum properties of the vortex strings. The explicit form of this
background field and the associated quantum vortex string correlation function
are derived. The complete expression for the quantum vortex creation operator
is explicitly obtained. We discuss the potential applicability of our results
in the physics of superfluids and rotating Bose-Einstein condensates.Comment: To appear in Journal of Physics A: Mathematical and Genera
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