1,226 research outputs found
Matrix Product States Algorithms and Continuous Systems
A generic method to investigate many-body continuous-variable systems is
pedagogically presented. It is based on the notion of matrix product states
(so-called MPS) and the algorithms thereof. The method is quite versatile and
can be applied to a wide variety of situations. As a first test, we show how it
provides reliable results in the computation of fundamental properties of a
chain of quantum harmonic oscillators achieving off-critical and critical
relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use
it to study the ground state properties of the quantum rotor model in one
spatial dimension, a model that can be mapped to the Mott insulator limit of
the 1-dimensional Bose-Hubbard model. At the quantum critical point, the
central charge associated to the underlying conformal field theory can be
computed with good accuracy by measuring the finite-size corrections of the
ground state energy. Examples of MPS-computations both in the finite-size
regime and in the thermodynamic limit are given. The precision of our results
are found to be comparable to those previously encountered in the MPS studies
of, for instance, quantum spin chains. Finally, we present a spin-off
application: an iterative technique to efficiently get numerical solutions of
partial differential equations of many variables. We illustrate this technique
by solving Poisson-like equations with precisions of the order of 10^(-7).Comment: 22 pages, 14 figures, final versio
Nernst effect in semi-metals: the meritorious heaviness of electrons
We present a study of electric, thermal and thermoelectric transport in
elemental Bismuth, which presents a Nernst coefficient much larger than what
was found in correlated metals. We argue that this is due to the combination of
an exceptionally low carrier density with a very long electronic
mean-free-path. The low thermomagnetic figure of merit is traced to the
lightness of electrons. Heavy-electron semi-metals, which keep a metallic
behavior in presence of a magnetic field, emerge as promising candidates for
thermomagnetic cooling at low temperatures.Comment: 4 pages, including 4 figure
Density matrix renormalization group in a two-dimensional Hamiltonian lattice model
Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional
model. Spontaneous breakdown of discrete symmetry is
studied numerically using vacuum wavefunctions. We obtain the critical coupling
and the critical exponent
, which are consistent with the Monte Carlo and the
exact results, respectively. The results are based on extrapolation to the
continuum limit with lattice sizes , and 1000. We show that the
lattice size L=500 is sufficiently close to the the limit .Comment: 16 pages, 10 figures, minor corrections, accepted for publication in
JHE
Nonperturbative renormalization group in a light-front three-dimensional real scalar model
The three-dimensional real scalar model, in which the symmetry
spontaneously breaks, is renormalized in a nonperturbative manner based on the
Tamm-Dancoff truncation of the Fock space. A critical line is calculated by
diagonalizing the Hamiltonian regularized with basis functions. The marginal
() coupling dependence of the critical line is weak. In the broken
phase the canonical Hamiltonian is tachyonic, so the field is shifted as
. The shifted value is determined as a function of
running mass and coupling so that the mass of the ground state vanishes.Comment: 23 pages, LaTeX, 6 Postscript figures, uses revTeX and epsbox.sty. A
slight revision of statements made, some references added, typos correcte
Variational Calculation of the Effective Action
An indication of spontaneous symmetry breaking is found in the
two-dimensional model, where attention is paid to the
functional form of an effective action. An effective energy, which is an
effective action for a static field, is obtained as a functional of the
classical field from the ground state of the hamiltonian interacting
with a constant external field. The energy and wavefunction of the ground state
are calculated in terms of DLCQ (Discretized Light-Cone Quantization) under
antiperiodic boundary conditions. A field configuration that is physically
meaningful is found as a solution of the quantum mechanical Euler-Lagrange
equation in the limit. It is shown that there exists a nonzero field
configuration in the broken phase of symmetry because of a boundary
effect.Comment: 26 pages, REVTeX, 7 postscript figures, typos corrected and two
references adde
Pressure dependence of the thermoelectric power of single-walled carbon nanotubes
We have measured the thermoelectric power (S) of high purity single-walled
carbon nanotube mats as a function of temperature at various hydrostatic
pressures up to 2.0 GPa. The thermoelectric power is positive, and it increases
in a monotonic way with increasing temperature for all pressures. The low
temperature (T < 40 K) linear thermoelectric power is pressure independent and
is characteristic for metallic nanotubes. At higher temperatures it is enhanced
and though S(T) is linear again above about 100 K it has a nonzero intercept.
This enhancement is strongly pressure dependent and is related to the change of
the phonon population with hydrostatic pressure.Comment: 4 pages, 3 figure
Pattern formation
The Pattern Formation problem is one of the most important coordination problem for robotic systems. Initially the entities are in arbitrary positions; within finite time they must arrange themselves in the space so to form a pattern given in input. In this chapter, we will mainly deal with the problem in the OBLOT model
A New Basis Function Approach to 't Hooft-Bergknoff-Eller Equations
We analytically and numerically investigate the 't Hooft-Bergknoff-Eller
equations, the lowest order mesonic Light-Front Tamm-Dancoff equations for
U(N_C) and SU(N_C) gauge theories. We find the wavefunction can be well
approximated by new basis functions and obtain an analytic formula for the mass
of the lightest bound state. Its value is consistent with the precedent
results.Comment: 16 pages, 3 figure
Exact solutions to chaotic and stochastic systems
We investigate functions that are exact solutions to chaotic dynamical
systems. A generalization of these functions can produce truly random numbers.
For the first time, we present solutions to random maps. This allows us to
check, analytically, some recent results about the complexity of random
dynamical systems. We confirm the result that a negative Lyapunov exponent does
not imply predictability in random systems. We test the effectiveness of
forecasting methods in distinguishing between chaotic and random time-series.
Using the explicit random functions, we can give explicit analytical formulas
for the output signal in some systems with stochastic resonance. We study the
influence of chaos on the stochastic resonance. We show, theoretically, the
existence of a new type of solitonic stochastic resonance, where the shape of
the kink is crucial. Using our models we can predict specific patterns in the
output signal of stochastic resonance systems.Comment: 31 pages, 18 figures (.eps). To appear in Chaos, March 200
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