SCALING LIMIT FOR GIBBS STATES OF JOHNSON GRAPHS AND RESULTING MEIXNER CLASSES

2003 ◽  
Vol 06 (01) ◽  
pp. 139-143 ◽  
Author(s):  
AKIHITO HORA
Keyword(s):  
Fock Space ◽  
Gibbs State ◽  
Scaling Limit ◽  
Temperature Limit ◽  
Zero Temperature ◽  
Johnson Graph ◽  
Meixner Polynomials ◽  
Johnson Graphs ◽  
The One ◽  
Interacting Fock Space

Asymptotic behavior of spectral distribution of the adjacency operator on the Johnson graph with respect to the Gibbs state is discussed in infinite volume and zero temperature limit. The limit picture is drawn on the one-mode interacting Fock space associated with Meixner polynomials.

scholarly journals Large deviations for quantum spin probabilities at temperature zero

2018 ◽  
Vol 18 (06) ◽  
pp. 1850044 ◽  
Author(s):  
Artur O. Lopes ◽  
Jairo K. Mengue ◽  
Joana Mohr ◽  
Carlos G. Moreira
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Gibbs State ◽  
Temperature Limit ◽  
Quantum Spin ◽  
Stationary Probability ◽  
Zero Temperature ◽  
Spin Lattice ◽  
Almost Everywhere ◽  
Class Of Functions

We consider certain self-adjoint observable for the KMS state associated to the Hamiltonian [Formula: see text] over the quantum spin lattice [Formula: see text]. For a fixed observable of the form [Formula: see text], where [Formula: see text], and for the zero temperature limit one can get a naturally defined stationary probability [Formula: see text] on the Bernoulli space [Formula: see text]. This probability is ergodic but it is not mixing for the shift map. It is not a Gibbs state for a continuous normalized potential but its Jacobian assume only two values almost everywhere. Anyway, for such probability [Formula: see text] we can show that a Large Deviation Principle is true for a certain class of functions. The result is derived by showing the explicit form of the free energy which is differentiable.

WHITE NOISE LÉVY–MEIXNER PROCESSES THROUGH A TRANSFER PRINCIPAL FROM ONE-MODE TO ONE-MODE TYPE INTERACTING FOCK SPACES

2010 ◽  
Vol 13 (03) ◽  
pp. 435-460 ◽  
Author(s):  
LUIGI ACCARDI ◽  
ABDESSATAR BARHOUMI ◽  
ANIS RIAHI
Keyword(s):  
White Noise ◽  
Fock Space ◽  
Delta Function ◽  
Fock Spaces ◽  
Jacobi Fields ◽  
Derivative Formula ◽  
Scalar Products ◽  
The Fourier Transform ◽  
The One ◽  
Interacting Fock Space

Consider the Lévy–Meixner one-mode interacting Fock space {ΓLM, 〈 ⋅, ⋅ 〉LM}. Inspired by a derivative formula appearing in 〈 ⋅, ⋅ 〉LM, we define scalar products 〈 ⋅, ⋅ 〉LM , nin symmetric n-particle spaces. Then, we introduce a class of one-mode type interacting Fock spaces [Formula: see text] naturally associated to the one-dimensional infinitely divisible distributions with Lévy–Meixner type {μr; r > 0}. The Fourier transform in generalized joint eigenvectors of a family [Formula: see text] of Lévy–Meixner Jacobi fields provides a way to explicit a unitary isomorphism 𝔘LMbetween [Formula: see text] and the so-called Lévy–Meixner white noise space [Formula: see text]. We derive a chaotic decomposition property of the quadratic integrable functionals of the Lévy–Meixner white noise processes in terms of an appropriate Wick tensor product. For their stochastic regularity, we give explicit form and sharp estimate of the associated Donsker's delta function.

ON THE QUADRATIC HEISENBERG GROUP

2010 ◽  
Vol 13 (04) ◽  
pp. 551-587 ◽  
Author(s):  
LUIGI ACCARDI ◽  
HABIB OUERDIANE ◽  
HABIB REBEÏ
Keyword(s):  
White Noise ◽  
Heisenberg Group ◽  
Lie Group ◽  
Unitary Operator ◽  
Fock Space ◽  
Local Chart ◽  
Rational Expression ◽  
The One ◽  
Interacting Fock Space ◽  
Group Law

In this paper we introduce the quadratic Weyl operators canonically associated to the one mode renormalized square of white noise (RSWN) algebra as unitary operator acting on the one mode interacting Fock space {Γ, {ωn, n ∈ ℕ}, Φ} where {ωn, n ∈ ℕ} is the principal Jacobi sequence of the nonstandard (i.e. neither Gaussian nor Poisson) Meixner classes. We deduce the quadratic Weyl relations and construct the quadratic analogue of the Heisenberg Lie group with one degree of freedom. In particular, we determine the manifold structure of the group and introduce a local chart containing the identity on which the group law has a simple rational expression in the chart coordinates (see Theorem 6.3).

ANALYTIC CHARACTERIZATION OF ONE-MODE INTERACTING FOCK SPACE

2001 ◽  
Vol 04 (03) ◽  
pp. 409-415 ◽  
Author(s):  
NOBUHIRO ASAI
Keyword(s):  
Fock Space ◽  
Integral Transformation ◽  
Representation Space ◽  
The One ◽  
Interacting Fock Space ◽  
Bargmann Representation

In this paper, we shall give the Segal–Bargmann representation space of the one-mode interacting Fock space. For this purpose, we shall define the generalized coherent vector associated with the Szegö–Jacobi parameters and introduce the associated integral transformation.

scholarly journals Dissipation of Quantum Turbulence in the Zero Temperature Limit

2007 ◽  
Vol 99 (26) ◽  
Author(s):  
P. M. Walmsley ◽  
A. I. Golov ◽  
H. E. Hall ◽  
A. A. Levchenko ◽  
W. F. Vinen
Keyword(s):  
Quantum Turbulence ◽  
Temperature Limit ◽  
Zero Temperature

AN IMPROVED ONE-LOOP ANALYSIS OF THE λϕ4 THEORY AT FINITE TEMPERATURE

1987 ◽  
Vol 02 (03) ◽  
pp. 713-728 ◽  
Author(s):  
SWEE-PING CHIA
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Loop Analysis ◽  
Temperature Dependent ◽  
Effective Coupling ◽  
Loop Approximation ◽  
The One ◽  
Dependent Mass

The λϕ4 theory with tachyonic mass is analyzed at T ≠ 0 using an improved one-loop approximation in which each of the bare propagators in the one-loop diagram is replaced by a dressed propagator to take into account the higher loop effects. The dressed propagator is characterized by a temperature-dependent mass which is determined by a self-consistent relation. Renomalization is found to be necessarily temperature-dependent. Real effective potential is obtained, giving rise to real effective mass and real coupling constant. For T < Tc, this is achieved by first shifting the ϕ field by its zero-temperature vacuum expectation value. The effective coupling constant is found to exhibit the striking behavior that it approaches a constant nonzero value as T → ∞.

scholarly journals Scaling limit of the one-dimensional XXZ Heisenberg chain with easy axis anisotropy

1999 ◽  
Vol 562 (3) ◽  
pp. 497-523 ◽  
Author(s):  
Tamás Hauer ◽  
Attila Rákos ◽  
Ferenc Woynarovich
Keyword(s):  
Easy Axis ◽  
Scaling Limit ◽  
Heisenberg Chain ◽  
One Dimensional ◽  
The One
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