Showing papers on "Coherent states in mathematical physics published in 2006"
TL;DR: For a q-deformed harmonic oscillator, the product of the coordinate-momentum uncertainties in q-oscillator eigenstates and coherent states was shown in this paper.
Abstract: For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We calculate the product of the “coordinate-momentum” uncertainties in q-oscillator eigenstates and in coherent states. For the oscillator, this product is minimum in the ground state and equals 1/2, as in the standard quantum mechanics. For coherent states, the q-deformation results in a violation of the standard uncertainty relation; the product of the coordinate-and momentum-operator uncertainties is always less than 1/2. States with the minimum uncertainty, which tends to zero, correspond to the values of λ near the convergence radius of the q-exponential.
45 citations
06 Mar 2006
TL;DR: In this paper, the recently developed coupled coherent states theory is applied to direct full dimensional simulation of tunneling in multidimensional systems, and it is shown that the efficiency of the technique is largely due to the use of quantum averaged potentials.
Abstract: The recently developed coupled coherent states theory is applied to direct full dimensional simulation of tunneling in multidimensional systems. The approach is shown to work well for both symmetric and asymmetric tunneling in up to 20 dimensions. We show that the efficiency of the technique is largely due to the use of quantum averaged potentials to guide a moving basis of coherent states.
32 citations
TL;DR: In this article, the authors use the formulation of the quantum mechanics of first-quantized Klein-Gordon fields given in the first series of this series of papers to study relativistic coherent states.
25 citations
TL;DR: In this article, the Gazeau-Klauder formalism was used to construct coherent states of non-Hermitian quantum systems, and the construction of coherent states following Klauder's minimal prescription.
16 citations
TL;DR: In this paper, a generalized q-deformed Heisenberg?Weyl algebra is used to obtain analytical expressions for a general class of qdeformed coherent states associated with the different patterns of the energy spectrum exhibited by the nonlinear f-oscillator.
Abstract: Adopting the framework of the generalized q-deformed Heisenberg?Weyl algebra , we present a mathematical procedure which leads us to obtain analytical expressions for a general class of q-deformed coherent states associated with the different patterns of the energy spectrum exhibited by the nonlinear f-oscillator. In particular, we establish the properties of a small group of q-deformed coherent states for ? > ? > 0 with emphasis on the resolution of unity. As an application of these properties, we investigate the Robertson?Schr?dinger uncertainty relation and the squeezing effect for the deformed coordinate and momentum operators, which are defined in terms of the abstract elements of this algebra. Furthermore, we also obtain the Wigner function and the correct quantum-mechanical marginal distributions in phase space.
12 citations
03 Jan 2006
TL;DR: An elementary introduction to the mathematical theory of coherent states is presented in this article, including some applications to different models of physical interest, and some applications for coherent states can be found in this paper.
Abstract: An elementary introduction to the mathematical theory of coherent states is presented, including some applications to different models of physical interest.
10 citations
TL;DR: In this paper, the definitions of para-Grassmann variables and q-oscillator algebras are re-called and some new properties are given, and a formula for the trace of a operator expressed as a function of the creation and annihilation operators is given.
Abstract: The definitions of para-Grassmann variables and q-oscillator algebras are re- called. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace of a operator expressed as a function of the creation and annihilation operators.
9 citations
TL;DR: In this paper, the (in)finite dimensional symplectic group of homogeneous canonical transformations is represented on the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states.
Abstract: The (in)finite dimensional symplectic group of homogeneous canonical transformations is represented on the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states.
8 citations
TL;DR: In this article, the quaternionic vector coherent states of the supersymmetric harmonic oscillator with broken symmetry were realized as coherent states, and the nonclassical properties of the oscillator, such as the photon number distribution and signal-to-quantum-noise ratio in terms of these states and discussed the squeezing properties and temporal stability of the coherent states.
Abstract: The quaternionic vector coherent states are realized as coherent states of the supersymmetric harmonic oscillator with broken symmetry in analogy with the standard canonical coherent states of the ordinary harmonic oscillator. We study the nonclassical properties of the oscillator, such as the photon number distribution and signal-to-quantum-noise ratio in terms of these states and discuss the squeezing properties and the temporal stability of the coherent states. We obtain the orthogonal polynomials associated with the quaternionic vector coherent states.
7 citations
TL;DR: In this article, the authors constructed the parametric-time coherent states for the negative energy states of the generalized MIC-Kepler system, in which a charged particle is in a monopole vector potential, a Coulomb potential, and a Bohm-Aharonov potantial.
Abstract: In this study, we construct the parametric-time coherent states for the negative energy states of the generalized MIC-Kepler system, in which a charged particle is in a monopole vector potential, a Coulomb potential, and a Bohm-Aharonov potantial. We transform the system into four isotropic harmonic oscillators and construct the parametric-time coherent states for these oscillators. Finally, we compactify these states into the physical time coherent states for the generalized MIC-Kepler system.
7 citations
TL;DR: In this article, a general theoretical formalism is presented to compute the fidelity of transformations of unknown quantum states, and the theory is applied to Gaussian transformations of continuous variable quantum systems.
Abstract: We present a general theoretical formalism to compute the fidelity of transformations of unknown quantum states, and we apply our theory to Gaussian transformations of continuous variable quantum systems. For the case of a Gaussian distribution of displaced coherent states, the theory is readily tractable by a covariance matrix formalism, and a wider class of states, exemplified by Fock states, can be treated efficiently by the Wigner function formalism. Given the distribution of input states, the optimum feedback gain is identified, and analytical results for the fidelities are presented for recently implemented teleportation and memory storage protocols for continuous variables.
TL;DR: In this article, it was shown that the Hamiltonian constraint operator employed currently in homogeneous LQC has a correct classical limit with respect to the coherent states of the quantum dynamics.
Abstract: Semiclassical states in homogeneous loop quantum cosmology (LQC) are constructed in two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semiclassical (coherent) state is obtained by solving the eigenequation of that operator. Moreover, we use these coherent states to analyse the semiclassical limit of the quantum dynamics. It turns out that the Hamiltonian constraint operator employed currently in homogeneous LQC has a correct classical limit with respect to the coherent states. In the second approach, the other kind of semiclassical state is derived from the mathematical construction of coherent states for compact Lie groups due to Hall.
03 Jan 2006
TL;DR: In this article, coherent states are constructed for one-dimensional Hamiltonians whose spectra are composed of an infinite number of discrete energy levels depending analytically on the index labeling them.
Abstract: Coherent states are constructed for one‐dimensional Hamiltonians whose spectra are composed of an infinite number of discrete energy levels depending analytically on the index labeling them. The harmonic oscillator and infinite well potentials are used to illustrate the technique.
TL;DR: In this article, the authors discuss how to decompose the Fock space of a many-fermion system embedded in two-dimensional square lattice, and present specific examples where they calculate the multiplicities which are the dimensions of the decomposed spaces.
Abstract: We discuss how to decompose the Fock space of a many-fermion system embedded in two-dimensional square lattice. Wefirst notice that the symmetry group inherent in the system is one of the two-dimensional space groups. We shortly review thecorresponding irreducible representations of the group. We then find the characters of the reducible representation of the many-fermion Fock space. Using the characters, we obtain the multiplicity of each irreducible representation contained in the Fock space of a fixed number of fermions. We present specific examples, where we calculate the multiplicities which are the dimensions of the decomposed spaces.
TL;DR: The role of the three-boson algebra in the theoretical construction of both logical states and operators for quantum computing is investigated in this article, where the computational basis consists of three orthonormal codewords obtained from the coherent states of the algebra.
Abstract: The role of the three-boson algebra in the theoretical construction of both logical states and operators for quantum computing is investigated. The computational basis consists of three orthonormal codewords obtained from the coherent states of the algebra. The gate and phase operators acting on the codewords are found, and the relation between their matrix representations in the Fock space and the fundamental representation of su(3) is discussed.
TL;DR: Using even and odd coherent states, the spin-type W state was defined in this article and a new scheme for testing fundamental aspects of quantum mechanics and refuting local hidden variable theory without using inequalities.
Abstract: Using even and odd coherent states, we define a new state, which is called the spin-type W state. With the spin-type W states, we provide a new scheme for testing fundamental aspects of quantum mechanics and refuting local hidden variable theory without using inequalities. Finally, a scheme for preparing the spin-type W states, and discussion of experimental possibility and the effect of the measurement on physical observables due to a close orthogonality of the two coherent states are given.
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TL;DR: In this article, the construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space.
Abstract: The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As example we consider the generalized oscillator connected with Krawtchouk polynomials.
TL;DR: In this paper, the authors extend the BCS paring model with equally spaced energy levels to a general one-dimensional spin-1/2 Heisenberg model, and find a new symmetry of energy spectrum between its subspace n and subspace L−n of the Fock space.
Abstract: We extend the BCS paring model with equally spaced energy levels to a general one-dimensional spin-1/2 Heisenberg model. The two well-known symmetries of the Heisenberg model, i.e. permutational and spin-inversion symmetries, no longer exist. However, when jointing these two operations together, we find a new symmetry of energy spectrum between its subspace n and subspace L−n of the Fock space. A rigorous proof is presented.