150 research outputs found
A simple topological model with continuous phase transition
In the area of topological and geometric treatment of phase transitions and
symmetry breaking in Hamiltonian systems, in a recent paper some general
sufficient conditions for these phenomena in -symmetric systems
(i.e. invariant under reflection of coordinates) have been found out. In this
paper we present a simple topological model satisfying the above conditions
hoping to enlighten the mechanism which causes this phenomenon in more general
physical models. The symmetry breaking is testified by a continuous
magnetization with a nonanalytic point in correspondence of a critical
temperature which divides the broken symmetry phase from the unbroken one. A
particularity with respect to the common pictures of a phase transition is that
the nonanalyticity of the magnetization is not accompanied by a nonanalytic
behavior of the free energy.Comment: 17 pages, 7 figure
Minimizing Higgs Potentials via Numerical Polynomial Homotopy Continuation
The study of models with extended Higgs sectors requires to minimize the
corresponding Higgs potentials, which is in general very difficult. Here, we
apply a recently developed method, called numerical polynomial homotopy
continuation (NPHC), which guarantees to find all the stationary points of the
Higgs potentials with polynomial-like nonlinearity. The detection of all
stationary points reveals the structure of the potential with maxima,
metastable minima, saddle points besides the global minimum. We apply the NPHC
method to the most general Higgs potential having two complex Higgs-boson
doublets and up to five real Higgs-boson singlets. Moreover the method is
applicable to even more involved potentials. Hence the NPHC method allows to go
far beyond the limits of the Gr\"obner basis approach.Comment: 9 pages, 4 figure
Statistics of conductance oscillations of a quantum dot in the Coulomb-blockade regime
The fluctuations and the distribution of the conductance peak spacings of a
quantum dot in the Coulomb-blockade regime are studied and compared with the
predictions of random matrix theory (RMT). The experimental data were obtained
in transport measurements performed on a semiconductor quantum dot fabricated
in a GaAs-AlGaAs heterostructure. It is found that the fluctuations in the peak
spacings are considerably larger than the mean level spacing in the quantum
dot. The distribution of the spacings appears Gaussian both for zero and for
non-zero magnetic field and deviates strongly from the RMT-predictions.Comment: 7 pages, 4 figure
Absence of bimodal peak spacing distribution in the Coulomb blockade regime
Using exact diagonalization numerical methods, as well as analytical
arguments, we show that for the typical electron densities in chaotic and
disordered dots the peak spacing distribution is not bimodal, but rather
Gaussian. This is in agreement with the experimental observations. We attribute
this behavior to the tendency of an even number of electrons to gain on-site
interaction energy by removing the spin degeneracy. Thus, the dot is predicted
to show a non trivial electron number dependent spin polarization. Experimental
test of this hypothesis based on the spin polarization measurements are
proposed.Comment: 13 pages, 3 figures, accepted for publication in PRL - a few small
change
Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories
The interplay rich between algebraic geometry and string and gauge theories
has recently been immensely aided by advances in computational algebra.
However, these symbolic (Gr\"{o}bner) methods are severely limited by
algorithmic issues such as exponential space complexity and being highly
sequential. In this paper, we introduce a novel paradigm of numerical algebraic
geometry which in a plethora of situations overcomes these short-comings. Its
so-called 'embarrassing parallelizability' allows us to solve many problems and
extract physical information which elude the symbolic methods. We describe the
method and then use it to solve various problems arising from physics which
could not be otherwise solved.Comment: 36 page
Statistical Analysis of Magnetic Field Spectra
We have calculated and statistically analyzed the magnetic-field spectrum
(the ``B-spectrum'') at fixed electron Fermi energy for two quantum dot systems
with classically chaotic shape. This is a new problem which arises naturally in
transport measurements where the incoming electron has a fixed energy while one
tunes the magnetic field to obtain resonance conductance patterns. The
``B-spectrum'', defined as the collection of values at which
conductance takes extremal values, is determined by a quadratic
eigenvalue equation, in distinct difference to the usual linear eigenvalue
problem satisfied by the energy levels. We found that the lower part of the
``B-spectrum'' satisfies the distribution belonging to Gaussian Unitary
Ensemble, while the higher part obeys a Poisson-like behavior. We also found
that the ``B-spectrum'' fluctuations of the chaotic system are consistent with
the results we obtained from random matrices
Manifestation of Quantum Chaos in Electronic Band Structures
We use semiconductors as an example to show that quantum chaos manifests
itself in the energy spectrum of crystals. We analyze the {\it ab initio} band
structure of silicon and the tight-binding spectrum of the alloy
, and show that some of their statistical properties obey the
universal predictions of quantum chaos derived from the theory of random
matrices. Also, the Bloch momenta are interpreted as external, tunable,
parameters, acting on the reduced (unit cell) Hamiltonian, in close analogy to
Aharonov-Bohm fluxes threading a torus. They are used in the investigation of
the parametric autocorrelator of crystal velocities. We find that our results
are in good agreement with the universal curves recently proposed by Simons and
coworkers.Comment: 15 pages with 6 Postscript figures included, RevTex-3, CMT-ERM/940
Numerical elimination and moduli space of vacua
We propose a new computational method to understand the vacuum moduli space of (supersymmetric) field theories. By combining numerical algebraic geometry (NAG) and elimination theory, we develop a powerful, efficient, and parallelizable algorithm toextract important information such as the dimension, branch structure, Hilbert series and subsequent operator counting, as well as variation according to coupling constants and mass parameters. We illustrate this method on a host of examples from gauge theory, string theory, and algebraic geometry
Density functional theory of spin-polarized disordered quantum dots
Using density functional theory, we investigate fluctuations of the ground
state energy of spin-polarized, disordered quantum dots in the metallic regime.
To compare to experiment, we evaluate the distribution of addition energies and
find a convolution of the Wigner-Dyson distribution, expected for noniteracting
electrons, with a narrower Gaussian distribution due to interactions. The tird
moment of the total distribution is independent of interactions, and so is
predicted to decrease by a factor of 0.405 upon application of a magnetic field
which transforms from the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 13 pages, 2 figure
Electron-Electron Interaction in Disordered Mesoscopic Systems: Weak Localization and Mesoscopic Fluctuations of Polarizability and Capacitance
The weak localization correction and the mesoscopic fluctuations of the
polarizability and the capacitance of a small disordered sample are studied
systematically in 2D and 3D geometries. While the grand canonical ensemble
calculation gives the positive magnetopolarizability, in the canonical ensemble
(appropriate for isolated samples) the sign of the effect is reversed. The
magnitude of mesoscopic fluctuations for a single sample exceeds considerably
the value of the weak localization correction.Comment: 13 pages Latex, 3 .eps figures included. To appear in Phys. Rev. B.
Minor corrections, in particular in formulae; new references adde
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