Representations of Coherent and Squeezed States in a $f$-deformed Fock Space

Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement

In this parer, q-deformed oscillator for pseudo-Hermitian systems is investigated and pseudo-Hermitian appropriate coherent and squeezed states are studied. Also, some basic properties of these states is surveyed. The over-completeness property of the para-Grassmannian pseudo-Hermitian coherent states (PGPHCSs) examined, and also the stability of coherent and squeezed states discussed. The pseudo-Hermitian supercoherent states as the product of a pseudo-Hermitian bosonic coherent state and a para-Grassmannian pseudo-Hermitian coherent state introduced, and the method also developed to define p…

From Fock's Transformation to de Sitter Space

As in Deformed Special Relativity, we showed recently that the Fock coordinate transformation can be derived from a new deformed Poisson brackets. This approach allowed us to establish the corresponding momentum transformation which keeps invariant the four dimensional contraction $p_μ x^μ $. From the resulting deformed algebra, we construct in this paper the corresponding first Casimir. After first quantization, we show by using the Klein-Gordon equation that the spacetime of the Fock transformation is the de Sitter one. As we will see, the invariant length representing the universe radius in…

Maths-type q-deformed coherent states for q > 1

Maths-type q-deformed coherent states with $q > 1$ allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both position and momentum and are intelligent coherent states for the corresponding deformed Heisenberg algebra.

Fock representations of $Q$-deformed commutation relations

We consider Fock representations of the $Q$-deformed commutation relations $$\partial_s\partial^†_t=Q(s,t)\partial_t^†\partial_s+δ(s,t), \quad s,t\in T.$$ Here $T:=\mathbb R^d$ (or more generally $T$ is a locally compact Polish space), the function $Q:T^2\to \mathbb C$ satisfies $|Q(s,t)|\le1$ and $Q(s,t)=\overline{Q(t,s)}$, and $$\int_{T^2}h(s)g(t)δ(s,t)\,σ(ds)σ(dt):=\int_T h(t)g(t)\,σ(dt),$$ $σ$ being a fixed reference measure on $T$. In the case where $|Q(s,t)|\equiv 1$, the $Q$-deformed commutation relations describe a generalized statistics studied by Liguori and Mintchev (1995). These ge…

扩展耦合SUSY、伪玻色子与弱压缩态

Extended coupled SUSY, pseudo-bosons and weak squeezed states

本文通过伪玻色子阶梯算符的平方构造满足变形su(1,1)李代数的本征态，分析其平方可积性与双正交性，并初步探讨双压缩态。

Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras

Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed bose and fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Green ansatz.

Time-dependent q-deformed coherent states for generalized uncertainty relations

We investigate properties of generalized time-dependent q-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg's uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e. the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest's theorem hold at all times. We conjecture that the model ex…

Generalized q-deformed Tamm-Dancoff oscillator algebra and associated coherent states

In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed $q-$number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics a…

阶乘 Fock 自由费米子

Factorial Fock free fermions

本文构造双参数形变的自由费米子流、Hamilton 量与顶点算子，将其关联至可解六顶点模型，并通过玻色–费米对应得到双阶乘 Schur 函数及二维 Toda 格 tau 函数解。