28,349 research outputs found

### Energy Spectra for Fractional Quantum Hall States

Fractional quantum Hall states (FQHS) with the filling factor nu = p/q of q <
21 are examined and their energies are calculated. The classical Coulomb energy
is evaluated among many electrons; that energy is linearly dependent on 1/nu.
The residual binding energies are also evaluated. The electron pair in nearest
Landau-orbitals is more affected via Coulomb transition than an electron pair
in non-nearest orbitals. Each nearest electron pair can transfer to some empty
orbital pair, but it cannot transfer to the other empty orbital pair because of
conservation of momentum. Counting the numbers of the allowed and forbidden
transitions, the binding energies are evaluated for filling factors of 126
fraction numbers. Gathering the classical Coulomb energy and the pair
transition energy, we obtain the spectrum of energy versus nu. This energy
spectrum elucidates the precise confinement of Hall resistance at specific
fractional filling factors.Comment: 5 pages, 3 figure

### Excited nucleon spectrum from lattice QCD with maximum entropy method

We study excited states of the nucleon in quenched lattice QCD with the
spectral analysis using the maximum entropy method. Our simulations are
performed on three lattice sizes $16^3\times 32$, $24^3\times 32$ and
$32^3\times 32$, at $\beta=6.0$ to address the finite volume issue. We find a
significant finite volume effect on the mass of the Roper resonance for light
quark masses. After removing this systematic error, its mass becomes
considerably reduced toward the direction to solve the level order puzzle
between the Roper resonance $N'(1440)$ and the negative-parity nucleon
$N^*(1535)$.Comment: Lattice2003(spectrum), 3 pages, 4 figure

### Evaluation of specific heat for superfluid helium between 0 - 2.1 K based on nonlinear theory

The specific heat of liquid helium was calculated theoretically in the Landau
theory. The results deviate from experimental data in the temperature region of
1.3 - 2.1 K. Many theorists subsequently improved the results of the Landau
theory by applying temperature dependence of the elementary excitation energy.
As well known, many-body system has a total energy of Galilean covariant form.
Therefore, the total energy of liquid helium has a nonlinear form for the
number distribution function. The function form can be determined using the
excitation energy at zero temperature and the latent heat per helium atom at
zero temperature. The nonlinear form produces new temperature dependence for
the excitation energy from Bose condensate. We evaluate the specific heat using
iteration method. The calculation results of the second iteration show good
agreement with the experimental data in the temperature region of 0 - 2.1 K,
where we have only used the elementary excitation energy at 1.1 K.Comment: 6 pages, 3 figures, submitted to Journal of Physics: Conference
Serie

### Relaxor ferroelectricity induced by electron correlations in a molecular dimer Mott insulator

We have investigated the dielectric response in an antiferromagnetic
dimer-Mott insulator beta'-(BEDT-TTF)2ICl2 with square lattice, compared to a
spin liquid candidate kappa-(BEDT-TTF)2Cu2(CN)3. Temperature dependence of the
dielectric constant shows a peak structure obeying Curie-Weiss law with strong
frequency dependence. We found an anisotropic ferroelectricity by pyrocurrent
measurements, which suggests the charge disproportionation in a dimer. The
ferroelectric actual charge freezing temperature is related to the
antiferromagnetic interaction, which is expected to the charge-spin coupled
degrees of freedom in the system.Comment: 5 pages, 4 figures, to be published in Phys. Rev.

### Signatures of S-wave bound-state formation in finite volume

We discuss formation of an S-wave bound-state in finite volume on the basis
of L\"uscher's phase-shift formula.It is found that although a bound-state pole
condition is fulfilled only in the infinite volume limit, its modification by
the finite size corrections is exponentially suppressed by the spatial extent
$L$ in a finite box $L^3$. We also confirm that the appearance of the S-wave
bound state is accompanied by an abrupt sign change of the S-wave scattering
length even in finite volume through numerical simulations. This distinctive
behavior may help us to discriminate the loosely bound state from the lowest
energy level of the scattering state in finite volume simulations.Comment: 25 pages, 30 figures; v2: typos corrected and two references added,
v3: final version to appear in PR

### Shape Invariant Potentials in "Discrete Quantum Mechanics"

Shape invariance is an important ingredient of many exactly solvable quantum
mechanics. Several examples of shape invariant ``discrete quantum mechanical
systems" are introduced and discussed in some detail. They arise in the problem
of describing the equilibrium positions of Ruijsenaars-Schneider type systems,
which are "discrete" counterparts of Calogero and Sutherland systems, the
celebrated exactly solvable multi-particle dynamics. Deformed Hermite and
Laguerre polynomials are the typical examples of the eigenfunctions of the
above shape invariant discrete quantum mechanical systems.Comment: 15 pages, 1 figure. Contribution to a special issue of Journal of
Nonlinear Mathematical Physics in honour of Francesco Calogero on the
occasion of his seventieth birthda

### Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics

Certain aspects of the integrability/solvability of the
Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen
systems with rational and trigonometric potentials are reviewed. The
equilibrium positions of classical multi-particle systems and the
eigenfunctions of single-particle quantum mechanics are described by the same
orthogonal polynomials: the Hermite, Laguerre, Jacobi, continuous Hahn, Wilson
and Askey-Wilson polynomials. The Hamiltonians of these single-particle quantum
mechanical systems have two remarkable properties, factorization and shape
invariance.Comment: 30 pages, 1 figure. Contribution to proceedings of RIMS workshop
"Elliptic Integrable Systems" (RIMS, Nov. 2004

### Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials

The equilibrium positions of the multi-particle classical
Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials
associated with the classical root systems are described by the classical
orthogonal polynomials; the Hermite, Laguerre and Jacobi polynomials. The
eigenfunctions of the corresponding single-particle quantum CSM systems are
also expressed in terms of the same orthogonal polynomials. We show that this
interesting property is inherited by the Ruijsenaars-Schneider-van Diejen
(RSvD) systems, which are integrable deformation of the CSM systems; the
equilibrium positions of the multi-particle classical RSvD systems and the
eigenfunctions of the corresponding single-particle quantum RSvD systems are
described by the same orthogonal polynomials, the continuous Hahn (special
case), Wilson and Askey-Wilson polynomials. They belong to the Askey-scheme of
the basic hypergeometric orthogonal polynomials and are deformation of the
Hermite, Laguerre and Jacobi polynomials, respectively. The Hamiltonians of
these single-particle quantum mechanical systems have two remarkable
properties, factorization and shape invariance.Comment: 16 pages, 1 figur

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