相关论文: Completeness of Coherent States Associated with Se…
The multiphoton coherent states, a generalization to coherent sates, are derived for electrons in bilayer graphene placed in a constant homogeneous magnetic field which is orthogonal to the bilayer surface. For that purpose a generalized…
The Kronecker theta function is a quotient of the Jacobi theta functions, which is also a special case of Ramanujan's $_1\psi_1$ summation. Using the Kronecker theta function as building blocks, we prove a decomposition theorem for theta…
We discuss reflections identities of harmonic sums up to weight three. The need for this kind of identities emerges in analysis of the general structure of eigenvalue of the BFKL equation. The reflection identities decompose a product of…
We construct generalized coherent states for the rationally extended Scarf-I potential. Statistical and geometrical properties of these states are investigated. Special emphasis is given to the study of spatio-temporal properties of the…
An identity by Ramanujan is expressed using polar coordinates, so that its proof reduces to the verification of an elementary trigonometric identity. This approach produces a few variations on Ramanujan's original identity.
We define a length function for a perfect crystal. As an application, we derive a variant of the Rogers-Ramanujan identities which involves (a $q$-analog of) the Fibonacci numbers.
In this work, we show that the completeness relation for the eigenvectors, which is an essential assumption of quantum mechanics, remains true if the Hamiltonian, having a discrete spectrum, is modified by a delta potential (to be made…
Entanglement characteristics of a pair coherent state is studied using entanglement of superposition. It is demonstrated only few states in the expansion of a pair coherent state, in a harmonic oscillator basis, contribute significantly to…
We present a systematic analysis on coherent states of composite bosons consisting of two distinguishable particles. By defining an effective composite boson (coboson) annihilation operator, we derive its eigenstate and commutator.…
The zeta function attached to a finite complex $X_\Gamma$ arising from the Bruhat-Tits building for $\PGL_3(F)$ was studied in \cite{KL}, where a closed form expression was obtained by a combinatorial argument. This identity can be…
When a superposition $(|\alpha>-|-\alpha>)$ of two coherent states with opposite phase falls upon a 50-50 beamsplitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of $\alpha$, as…
An eigenstate decoherence hypothesis states that each individual eigenstate of a large closed system is locally classical-like. We extend this hypothesis to account for a typically extremely short time scale of decoherence. The extension…
The celebrated Rogers-Ramanujan identities equate the number of integer partitions of $n$ ($n\in\mathbb N_0$) with parts congruent to $\pm 1 \pmod{5}$ (respectively $\pm 2 \pmod{5}$) and the number of partitions of $n$ with super-distinct…
Eigenvectors of the discrete Fourier transform can be expressed using Ramanujan theta functions. New theta function identities, Ramanujan theta function identities, and generating functions for the quadratic numbers are a consequence.
We investigate the superposition of coherent states, emphasizing quantum states with distinct Wigner phase-space features relevant to quantum information applications. In this study, we introduce generalized versions of the compass state,…
In earlier work a description of a physical entity is given by means of a state property system and it is proven that any state property system is equivalent to a closure space. In the present paper we investigate the relations between…
In this paper, we prove that there is a natural correspondence between product identities for theta functions and integer matrix exact covering systems. We show that since $\mathbb{Z}^n$ can be taken as the disjoint union of a lattice…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…
The beta integral is applied to accelerate the hypergeometric function $2 F 1\left\{1, B; C ; w\right\}$ to derive new infinite series for constants such as $\pi$ and values of the gamma function. A compendium of new infinite series is…
Coherent state path integrals are applied to a many-body problem for non-relativistic electrons in a central potential and an external magnetic field; however, in comparison to previous coherent state path integrals, we definitely fix the…