14,714 research outputs found
Quasi Exactly Solvable Difference Equations
Several explicit examples of quasi exactly solvable `discrete' quantum
mechanical Hamiltonians are derived by deforming the well-known exactly
solvable Hamiltonians of one degree of freedom. These are difference analogues
of the well-known quasi exactly solvable systems, the harmonic oscillator
(with/without the centrifugal potential) deformed by a sextic potential and the
1/sin^2x potential deformed by a cos2x potential. They have a finite number of
exactly calculable eigenvalues and eigenfunctions.Comment: LaTeX with amsfonts, no figure, 17 pages, a few typos corrected, a
reference renewed, 3/2 pages comments on hermiticity adde
Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
The annihilation-creation operators are defined as the
positive/negative frequency parts of the exact Heisenberg operator solution for
the `sinusoidal coordinate'. Thus are hermitian conjugate to each
other and the relative weights of various terms in them are solely determined
by the energy spectrum. This unified method applies to most of the solvable
quantum mechanics of single degree of freedom including those belonging to the
`discrete' quantum mechanics.Comment: 43 pages, no figures, LaTeX2e, with amsmath, amssym
Holographic Derivation of Entanglement Entropy from AdS/CFT
A holographic derivation of the entanglement entropy in quantum (conformal)
field theories is proposed from AdS/CFT correspondence. We argue that the
entanglement entropy in d+1 dimensional conformal field theories can be
obtained from the area of d dimensional minimal surfaces in AdS_{d+2},
analogous to the Bekenstein-Hawking formula for black hole entropy. We show
that our proposal perfectly reproduces the correct entanglement entropy in 2D
CFT when applied to AdS_3. We also compare the entropy computed in AdS_5 \times
S^5 with that of the free N=4 super Yang-Mills.Comment: 5 pages, 3 figures, Revtex, references adde
Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
We show that the equilibrium positions of the Ruijsenaars-Schneider-van
Diejen systems with the trigonometric potential are given by the zeros of the
Askey-Wilson polynomials with five parameters. The corresponding single
particle quantum version, which is a typical example of "discrete" quantum
mechanical systems with a q-shift type kinetic term, is shape invariant and the
eigenfunctions are the Askey-Wilson polynomials. This is an extension of our
previous study [1,2], which established the "discrete analogue" of the
well-known fact; The equilibrium positions of the Calogero systems are
described by the Hermite and Laguerre polynomials, whereas the corresponding
single particle quantum versions are shape invariant and the eigenfunctions are
the Hermite and Laguerre polynomials.Comment: 14 pages, 1 figure. The outline of derivation of the result in
section 2 is adde
Drinking patterns among Korean adults: results of the 2009 Korean community health survey.
ObjectivesIn Korea, the proportion of deaths due to alcohol is estimated at 8.9%, far exceeding the global estimate of 3.8%. Therefore, this study was performed to examine the factors associated with low-risk, moderate-risk, and high-risk drinking patterns in Korean adults and to identify target populations for prevention and control of alcohol-related diseases and deaths.MethodsWe analyzed data from 230 715 Korean adults aged 19 years and older who participated in the 2009 Korean Community Health Survey. Multinomial logistic regression analysis was used to examine associations between socio-demographic and health-related factors and patterns of alcohol use.ResultsA substantially larger proportion of men than women engaged in high risk (21.2% vs. 3.4%) and moderate-risk alcohol use (15.5% vs. 8.2%). In both sexes, moderate- and high-risk uses were associated with younger age, higher income, being currently employed, smoking, being overweight/obese, and good self-rated health.ConclusionsGiven the large proportion of the population that is engaging in moderate- and high-risk drinking and given the social norms that support this behavior, public health policies and campaigns to reduce alcohol consumption targeting the entire population are indicated
Growth of Magnetic Fields Induced by Turbulent Motions
We present numerical simulations of driven magnetohydrodynamic (MHD)
turbulence with weak/moderate imposed magnetic fields. The main goal is to
clarify dynamics of magnetic field growth. We also investigate the effects of
the imposed magnetic fields on the MHD turbulence, including, as a limit, the
case of zero external field. Our findings are as follows. First, when we start
off simulations with weak mean magnetic field only (or with small scale random
field with zero imposed field), we observe that there is a stage at which
magnetic energy density grows linearly with time. Runs with different numerical
resolutions and/or different simulation parameters show consistent results for
the growth rate at the linear stage. Second, we find that, when the strength of
the external field increases, the equilibrium kinetic energy density drops by
roughly the product of the rms velocity and the strength of the external field.
The equilibrium magnetic energy density rises by roughly the same amount.
Third, when the external magnetic field is not very strong (say, less than ~0.2
times the rms velocity when measured in the units of Alfven speed), the
turbulence at large scales remains statistically isotropic, i.e. there is no
apparent global anisotropy of order B_0/v. We discuss implications of our
results on astrophysical fluids.Comment: 16 pages, 18 figures; ApJ, accepte
Holographic classification of Topological Insulators and its 8-fold periodicity
Using generic properties of Clifford algebras in any spatial dimension, we
explicitly classify Dirac hamiltonians with zero modes protected by the
discrete symmetries of time-reversal, particle-hole symmetry, and chirality.
Assuming the boundary states of topological insulators are Dirac fermions, we
thereby holographically reproduce the Periodic Table of topological insulators
found by Kitaev and Ryu. et. al, without using topological invariants nor
K-theory. In addition we find candidate Z_2 topological insulators in classes
AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table
Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the
main parts of the eigenfunctions of new solvable discrete quantum mechanical
systems. Their orthogonality weight functions consist of quantum dilogarithm
functions, which are a natural extension of the Euler gamma functions and the
q-gamma functions (q-shifted factorials). The dimensions of the orthogonal
spaces are finite. These q-orthogonal polynomials are expressed in terms of the
Askey-Wilson polynomials and their certain limit forms.Comment: 37 pages. Comments and references added. To appear in J.Math.Phy
Orthogonal Polynomials from Hermitian Matrices
A unified theory of orthogonal polynomials of a discrete variable is
presented through the eigenvalue problem of hermitian matrices of finite or
infinite dimensions. It can be considered as a matrix version of exactly
solvable Schr\"odinger equations. The hermitian matrices (factorisable
Hamiltonians) are real symmetric tri-diagonal (Jacobi) matrices corresponding
to second order difference equations. By solving the eigenvalue problem in two
different ways, the duality relation of the eigenpolynomials and their dual
polynomials is explicitly established. Through the techniques of exact
Heisenberg operator solution and shape invariance, various quantities, the two
types of eigenvalues (the eigenvalues and the sinusoidal coordinates), the
coefficients of the three term recurrence, the normalisation measures and the
normalisation constants etc. are determined explicitly.Comment: 53 pages, no figures. Several sentences and a reference are added. To
be published in J. Math. Phy
Topological delocalization of two-dimensional massless Dirac fermions
The beta function of a two-dimensional massless Dirac Hamiltonian subject to
a random scalar potential, which e.g., underlies the theoretical description of
graphene, is computed numerically. Although it belongs to, from a symmetry
standpoint, the two-dimensional symplectic class, the beta function
monotonically increases with decreasing . We also provide an argument based
on the spectral flows under twisting boundary conditions, which shows that none
of states of the massless Dirac Hamiltonian can be localized.Comment: 4 pages, 2 figure
- âŠ