872 research outputs found
Bilinear identities on Schur symmetric functions
A series of bilinear identities on the Schur symmetric functions is obtained
with the use of Pluecker relations.Comment: Accepted to Journal of Nonlinear Mathematical Physics. A reference to
a connected result is adde
Analytical Form of the Deuteron Wave Function Calculated within the Dispersion Approach
We present a convenient analytical parametrization of the deuteron wave
function calculated within dispersion approach as a discrete superposition of
Yukawa-type functions, in both configuration and momentum spaces.Comment: 3 pages, 2 figure; several minor corrections adde
Entanglement in Valence-Bond-Solid States
This article reviews the quantum entanglement in Valence-Bond-Solid (VBS)
states defined on a lattice or a graph. The subject is presented in a
self-contained and pedagogical way. The VBS state was first introduced in the
celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki
(abbreviation AKLT is widely used). It became essential in condensed matter
physics and quantum information (measurement-based quantum computation). Many
publications have been devoted to the subject. Recently entanglement was
studied in the VBS state. In this review we start with the definition of a
general AKLT spin chain and the construction of VBS ground state. In order to
study entanglement, a block subsystem is introduced and described by the
density matrix. Density matrices of 1-dimensional models are diagonalized and
the entanglement entropies (the von Neumann entropy and Renyi entropy) are
calculated. In the large block limit, the entropies also approach finite
limits. Study of the spectrum of the density matrix led to the discovery that
the density matrix is proportional to a projector.Comment: Published version, 80 pages, 8 figures; references update
Quantum Interaction : the Construction of Quantum Field defined as a Bilinear Form
We construct the solution of the quantum wave equation
as a bilinear form which can
be expanded over Wick polynomials of the free -field, and where
is defined as the normal ordered product with
respect to the free -field. The constructed solution is correctly defined
as a bilinear form on , where is a
dense linear subspace in the Fock space of the free -field. On
the diagonal Wick symbol of this bilinear form
satisfies the nonlinear classical wave equation.Comment: 32 pages, LaTe
A holomorphic representation of the Jacobi algebra
A representation of the Jacobi algebra by first order differential operators with polynomial
coefficients on the manifold is presented. The
Hilbert space of holomorphic functions on which the holomorphic first order
differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the
Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI:
10.1142/S0129055X12920018, references update
Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
We characterize several phases of gapped spin systems by local order
parameters defined by quantized Berry phases. This characterization is
topologically stable against any small perturbation as long as the energy gap
remains finite. The models we pick up are dimerized Heisenberg chains
and S=2 Heisenberg chains with uniaxial single-ion-type anisotropy.
Analytically we also evaluate the topological local order parameters for the
generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) model. The relation between the
present Berry phases and the fractionalization in the integer spin chains are
discussed as well.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.
Deuteron tensor polarization component T_20(Q^2) as a crucial test for deuteron wave functions
The deuteron tensor polarization component T_20(Q^2) is calculated by
relativistic Hamiltonian dynamics approach. It is shown that in the range of
momentum transfers available in to-day experiments, relativistic effects, meson
exchange currents and the choice of nucleon electromagnetic form factors almost
do not influence the value of T_20(Q^2). At the same time, this value depends
strongly on the actual form of the deuteron wave function, that is on the model
of NN-interaction in deuteron. So the existing data for T_20(Q^2) provide a
crucial test for deuteron wave functions.Comment: 11 pages, 3 figure
Oscillatory regime in the Multidimensional Homogeneous Cosmological Models Induced by a Vector Field
We show that in multidimensional gravity vector fields completely determine
the structure and properties of singularity. It turns out that in the presence
of a vector field the oscillatory regime exists in all spatial dimensions and
for all homogeneous models. By analyzing the Hamiltonian equations we derive
the Poincar\'e return map associated to the Kasner indexes and fix the rules
according to which the Kasner vectors rotate. In correspondence to a
4-dimensional space time, the oscillatory regime here constructed overlap the
usual Belinski-Khalatnikov-Liftshitz one.Comment: 9 pages, published on Classical and Quantum Gravit
Multiplicity, Invariants and Tensor Product Decomposition of Tame Representations of U(\infty)
The structure of r-fold tensor products of irreducible tame representations
of the inductive limit U(\infty) of unitary groups U(n) are are described,
versions of contragredient representations and invariants are realized on
Bargmann-Segal-Fock spaces.Comment: 48 pages, LaTeX file, to appear in J. Math. Phy
Entanglement in a Valence-Bond-Solid State
We study entanglement in Valence-Bond-Solid state. It describes the ground
state of Affleck, Kennedy, Lieb and Tasaki quantum spin chain. The AKLT model
has a gap and open boundary conditions. We calculate an entropy of a subsystem
(continuous block of spins). It quantifies the entanglement of this block with
the rest of the ground state. We prove that the entanglement approaches a
constant value exponentially fast as the size of the subsystem increases.
Actually we proved that the density matrix of the continuous block of spins
depends only on the length of the block, but not on the total size of the chain
[distance to the ends also not essential]. We also study reduced density
matrices of two spins both in the bulk and on the boundary. We evaluated
concurrencies.Comment: 4pages, no figure
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