27,001 research outputs found

### Exact solution of one class of Maryland model

The Hamiltonian H of one-body Maryland model is defined as the sum of a
linear unperturbed Hamiltonian H_0 and the interaction V, which is a Toeplitz
matrix. Maryland model with a doubly infinite Hilbert space are exactly solved.
Special cases of one-body Maryland model include the original Maryland model
(Phys. Rev. Lett. 49, 833 (1982) and Physica 10D, 369 (1984)), which describes
a quantum kickied linear rotator and single band Bloch oscillations. Maryland
model and single band Bloch oscillations are the same Hamiltonian in two
different representations. A special case of many-body Maryland model is
Luttinger model.Comment: 5 pages, no figure

### General Theory of the Quantum Kicked Rotator. I

This is the first of a series of two papers. We discuss some basic problems
of the quantum kicked rotator (QKR) and review some important results in the
literature. We point out the flaws in the inverse Cayley transform method to
prove dynamic localization. When $\tau/2\pi$, where $\tau$ is the kick period,
is very close to a rational number, the localization length is larger than the
typical localization length. We analytically prove anomalous localization and
confirm it by numerical calculations. We point out open problems that need
further work.Comment: 10 pages, 6 figure

### Some new results on permutation polynomials over finite fields

Permutation polynomials over finite fields constitute an active research area
and have applications in many areas of science and engineering. In this paper,
four classes of monomial complete permutation polynomials and one class of
trinomial complete permutation polynomials are presented, one of which confirms
a conjecture proposed by Wu et al. (Sci. China Math., to appear. Doi:
10.1007/s11425-014-4964-2). Furthermore, we give two classes of trinomial
permutation polynomials, and make some progress on a conjecture about the
differential uniformity of power permutation polynomials proposed by Blondeau
et al. (Int. J. Inf. Coding Theory, 2010, 1, pp. 149-170).Comment: 21 pages. We have changed the title of our pape

### Non-convex Penalty for Tensor Completion and Robust PCA

In this paper, we propose a novel non-convex tensor rank surrogate function
and a novel non-convex sparsity measure for tensor. The basic idea is to
sidestep the bias of $\ell_1-$norm by introducing concavity. Furthermore, we
employ the proposed non-convex penalties in tensor recovery problems such as
tensor completion and tensor robust principal component analysis, which has
various real applications such as image inpainting and denoising. Due to the
concavity, the models are difficult to solve. To tackle this problem, we devise
majorization minimization algorithms, which optimize upper bounds of original
functions in each iteration, and every sub-problem is solved by alternating
direction multiplier method. Finally, experimental results on natural images
and hyperspectral images demonstrate the effectiveness and efficiency of the
proposed methods

### Competition between phase coherence and correlation in a mixture of Bose-Einstein condensates

Two-species hard-core bosons trapped in a three-dimensional isotropic
harmonic potential are studied with the path-integral quantum Monte Carlo
simulation. The double condensates show two distinct structures depending on
how the external potentials are set. Contrary to the mean-field results, we
find that the heavier particles form an outer shell under an identical external
potential whereas the lighter particles form an outer shell under the equal
energy spacing condition. Phase separations in both the spatial and energy
spaces are observed. We provide physical interpretations of these phase
separations and suggest future experiment to confirm these findings.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

### Condensate-profile asymmetry of a boson mixture in a disk-shaped harmonic trap

A mixture of two types of hard-sphere bosons in a disk-shaped harmonic trap
is studied through path-integral quantum Monte Carlo simulation at low
temperature. We find that the system can undergo a phase transition to break
the spatial symmetry of the model Hamiltonian when some of the model parameters
are varied. The nature of such a phase transition is analyzed through the
particle distributions and angular correlation functions. Comparisons are made
between our calculations and the available mean-field results on similar
models. Possible future experiments are suggested to verify our findings.Comment: 4 pages, 4 figure

### Global Level Number Variance in Integrable Systems

We study previously un-researched second order statistics - correlation
function of spectral staircase and global level number variance - in generic
integrable systems with no extra degeneracies. We show that the global level
number variance oscillates persistently around the saturation spectral
rigidity. Unlike other second order statistics - including correlation function
of spectral staircase - which are calculated over energy scales much smaller
than the running spectral energy, these oscillations cannot be explained within
the diagonal approximation framework of the periodic orbit theory. We give
detailed numerical illustration of our results using four integrable systems:
rectangular billiard, modified Kepler problem, circular billiard and elliptic
billiard.Comment: 5 pages, 3 figure

### Elliptic billiard - a non-trivial integrable system

We investigate the semiclassical energy spectrum of quantum elliptic
billiard. The nearest neighbor spacing distribution, level number variance and
spectral rigidity support the notion that the elliptic billiard is a generic
integrable system. However, second order statistics exhibit a novel property of
long-range oscillations. Classical simulation shows that all the periodic
orbits except two are not isolated. In Fourier analysis of the spectrum, all
the peaks correspond to periodic orbits. The two isolated periodic orbits have
small contribution to the fluctuation of level density, while non-isolated
periodic orbits have the main contribution. The heights of the majority of the
peaks match our semiclassical theory except for type-O periodic orbits.
Elliptic billiard is a nontrivial integrable system that will enrich our
understanding of integrable systems.Comment: 5 pages, 6 figure

### A Model for Stock Returns and Volatility

We prove that Student's t-distribution provides one of the better fits to
returns of S&P component stocks and the generalized inverse gamma distribution
best fits VIX and VXO volatility data. We further argue that a more accurate
measure of the volatility may be possible based on the fact that stock returns
can be understood as the product distribution of the volatility and normal
distributions. We find Brown noise in VIX and VXO time series and explain the
mean and the variance of the relaxation times on approach to the steady-state
distribution.Comment: 17 pages, 30 figures, 2 table

### Spectral and Parametric Averaging for Integrable Systems

We analyze two theoretical approaches to ensemble averaging for integrable
systems in quantum chaos - spectral averaging and parametric averaging. For
spectral averaging, we introduce a new procedure - rescaled spectral averaging.
Unlike traditional spectral averaging, it can describe the correlation function
of spectral staircase and produce persistent oscillations of the interval level
number variance. Parametric averaging, while not as accurate as rescaled
spectral averaging for the correlation function of spectral staircase and
interval level number variance, can also produce persistent oscillations of the
global level number variance and better describes saturation level rigidity as
a function of the running energy. Overall, it is the most reliable method for a
wide range of statistics.Comment: 7 pages, 7 figure

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