Coherent State Formalism Research Articles

Energy surfaces of 100–106Ru isotopes in the U(5)↔SO(9) transitional region

The critical behavior of 100–106Ru isotopes is investigated in the U(5)↔SO(9) transitional region of the spd-interacting boson model. We have developed a solvable extended transitional Hamiltonian based on affine SU(1,1) Lie algebra within the framework of the spd-interacting boson model. Also, we have used the catastrophe theory in combination with coherent state formalism to generate the energy surfaces of considered isotopes. The parameters of the transitional Hamiltonian are determined via Least-Square Fitting (LSF) to the experimental data of Ru isotopes to describe both positive and negative parity states and also E(1) and E(2) transition probabilities. Results describe experimental counterparts with satisfactory degrees of agreement and also suggest 100Ru as the best candidate for the critical point of this transitional region.

Energy spectra and E2 transition rates of 124—130Ba

In this paper, we have studied the energy spectra and [Formula: see text] values of [Formula: see text]Ba isotopes in the shape phase transition region between the spherical and gamma unstable deformed shapes. We have used a transitional interacting Boson model (IBM), Hamiltonian which is based on affine SU(1,1) Lie algebra in the both IBM-1 and 2 versions and also the Catastrophe theory in combination with a coherent state formalism to generate energy surfaces and determine the exact values of control parameters. Our results for control parameters suggest a combination of [Formula: see text](5) and SO(6) dynamical symmetries in this isotopic chain. Also, the theoretical predictions can be rather well reproduce the experimental counterparts, when the control parameter is approached to the SO(6) limit.

Multipion correlations induced by isospin conservation of coherent emission

Recent measurements have revealed a significant suppression of multipion Bose-Einstein correlations in heavy-ion collisions at the LHC. The suppression may be explained by postulating coherent pion emission. Typically, the suppression of Bose-Einstein correlations due to coherence is taken into account with the coherent state formalism in quantum optics. However, since charged pion correlations are most often measured, the additional constraint of isospin conservation, which is absent in quantum optics, needs to be taken into account. As a consequence, correlations emerge between pions of opposite charge. A calculation of the correlations induced by isospin conservation of coherent emission is made for two, three- and four-pion correlation functions and compared to the data from the LHC.

Study of Yb isotopes with the coherent state formalism

Coherent state approach (CSA) is applied to the interacting boson model (IBM) in the rotational region. States of the [Formula: see text] particle system are built up in a most general form as a function of the shape parameters [Formula: see text] and [Formula: see text]. The parameter [Formula: see text] occurring in the quadrupole operator which determines the degree of the [Formula: see text]-softness is taken to be varying with the boson number. The excitation energy equations are formed by using the moment of inertia of a rotating system which is obtained from the solution of the cranking problem. For each isotope, the deformation parameter is found by minimizing the ground state energy equation. The results are used to fit the experimental excitation energy spectrum and the electric quadrupole transition ratios of Yb isotopes. It is found that CSA works well to predict the energy of the states up to [Formula: see text]. But the predictions about the electric quadrupole transitions are nearly [Formula: see text] times greater than the experimental data.

Phase transition studies of the odd-mass 123−135Xe isotopes based on SU(1,1) algebra in IBFM

In this paper, we have investigated the positive-parity states in the odd-mass transitional [Formula: see text]Xe isotopes within the framework of the interacting boson–fermion model. Two solvable extended transitional Hamiltonians which are based on SU(1,1) algebra are employed to provide an investigation of quantum phase transition (QPT) between the spherical and deformed gamma — unstable shapes along the chain of Xe isotopes. The low-states energy spectra and B(E2) values for these nuclei have been calculated and compared with the experimental data. The predicted excitation energies and B(E2) transition rates of the odd isotopes are found to agree well with the experimental data. We have also analyzed the critical behavior of even–odd Xe isotopes via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces and special isotopes which are the best candidates for the critical point are identified.

Evolution of ground state nuclear shapes in tungsten nuclei in terms of interacting boson model

The tungsten nuclei 180–190W are investigated within the framework of the interacting boson model using an intrinsic coherent state formalism. The Hamiltonian operator contains only multipole operators of the subalgebra associated with the dynamical symmetries SU(3) and O(6). The study includes the behavior of potential energy surfaces (BES’s) and critical points in the space of the model parameters to declare the geometric character of the tungsten isotopic chain. Some selected energy levels and reduced E2 transition probabilities B(E2) for each nucleus are calculated to adjust the model parameters by using a computer code PH INT and simulated computer fitting programme to fit the experimental data with the IBM calculation by minimizing the root mean square deviations. The 180–190W isotopes lies in shape transition SU(3)-O(6) region of the IBM such that the lighter isotopes comes very clare to the SU(3) limit, while the behavior ones tend to be near the γ-unstable O(6) limit.

Generalization of coherent state quantization in higher dimensional de Sitter space

We have shown coherent state quantization of a particle in a maximally symmetric curved space-time i.e. in de Sitter space. As the coherent states are eigenvectors of the lowering operators, we have constructed the raising and lowering operators with the help of recurrence relation satisfied by the associated Legendre polynomial. These lowering operators have been used to describe an explicit form of coherent states followed by coherent states quantization in two-dimensional de Sitter space. Coherent states and their quantization are also generalized in D-dimensional de Sitter space.

Algebraic and group treatments to nonlinear displaced number states and their nonclassicality features: A new approach

Recently, nonlinear displaced number states (NDNSs) have been manually introduced, in which the deformation function f(n) has been artificially added to the previously well-known displaced number states (DNSs). Indeed, just a simple comparison has been performed between the standard coherent state and nonlinear coherent state for the formation of NDNSs. In the present paper, after expressing enough physical motivation of our procedure, four distinct classes of NDNSs are presented by applying algebraic and group treatments. To achieve this purpose, by considering the DNSs and recalling the nonlinear coherent states formalism, the NDNSs are logically defined through an algebraic consideration. In addition, by using a particular class of Gilmore–Perelomov-type of SU(1, 1) and a class of SU(2) coherent states, the NDNSs are introduced via group-theoretical approach. Then, in order to examine the nonclassical behavior of these states, sub-Poissonian statistics by evaluating Mandel parameter and Wigner quasi-probability distribution function associated with the obtained NDNSs are discussed, in detail.

On semi-classical limit of nonlinear quantum scattering

We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and the nonlinearity are asymptotically negligible for large time. Then, for data under the form of coherent state, we show that a scattering theory is also available for the approximate envelope of the propagated coherent state, which is given by a nonlinear equation. In the semi-classical limit, these two scattering operators can be compared in terms of classical scattering the-ory, thanks to a uniform in time error estimate. Finally, we infer a large time decoupling phenomenon in the case of finitely many initial coherent states.

Application of Coherent State Approach for the Cancellation of Infrared Divergences to All Orders in LFQED

We sketch an all order proof of cancellation of infrared (IR) divergences in Light Front Quantum Electrodynamics (LFQED) using a coherent state formalism. In this talk, it has been shown that the true IR divergences in fermion self energy are eliminated to all orders in a light-front time-ordered perturbative calculation if one uses coherent state basis instead of the usual Fock basis to calculate the Hamiltonian matrix elements.

Investigation of shape phase transition in the U(5) ↔ SO(6) transitional region by catastrophe theory and critical exponents of some quantities

In this paper, we have analyzed the critical behavior of even–even Ru and Pd isotopes between U(5) and SO(6) limits of interacting boson model via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces. The parameters of the Hamiltonian are determined via least-square fitting to the experimental data for different Ru and Pd isotopes. Our results suggest a second-order phase transition in these isotopic chains and propose the best candidates for E(5) critical symmetry. Also, the analogy between the critical exponents of ground state quantum phase transition and Landau values for the critical exponents of thermodynamic phase transitions are described.

On the coherent behavior of pancreatic beta cell clusters

Beta cells in pancreas represent an example of coupled biological oscillators which via communication pathways, are able to synchronize their electrical activity, giving rise to pulsatile insulin release. In this work we numerically analyze scale free self-similarity features of membrane voltage signal power density spectrum, through a stochastic dynamical model for beta cells in the islets of Langerhans fine tuned on mouse experimental data. Adopting the algebraic approach of coherent state formalism, we show how coherent molecular domains can arise from proper functional conditions leading to a parallelism with "phase transition" phenomena of field theory.

Coherent qubits stability and quantum phase transitions in the Lipkin–Meshkov–Glick model

The understanding and manipulation of information at quantum level requires an adequate treatment of phenomena such as qubits stability, singular behavior of Fidelity evolution at the event of quantum phase tran- sitions, tunneling, and parametric dependence of physical observables, such as the magnetization, under control variables manipulation. In the present work we consider the Lipkin-Meshkov-Glick model Hamiltonian, useful in the treatment of a kind of single-molecule magnets. Phase transition behavior is treated by means of catastrophe theory. We show that quantum and semiclassical behavior are completely organized by the separatrix of the system. Catastrophe theory and the coherent states formalism represent powerful tools in the analytical treatment of quan- tum information and its semiclassical behavior. Coherent states of the model demonstrate their importance at the semiclassic critical points. In particular, these states represent very closely the ground state of the system. Coherent qubit states are introduced by means of the coherent state representation of the system states. Singular character of Fidelity, due to tunneling at a phase transition point, can be numerically adjusted very closely to a Lorentzian curve.

Coherent States Formalism Applied to the Quantum Well Model

The different nanostructures (quantum dots, wires and wells) have specific properties which differ from those of the corresponding bulk structures. This fact leads to many applications in several branches of physics. In the paper we examine the behavior of a quantum system (a free particle and a quantum free particle gas) trapped inside the infinite quantum well, by using the coherent states formalism. Our approach is based on the fact that the dynamical group associated with the infinite quantum well is SU(1, 1), with the Bargmann index k = 1/2. These coherent states always have the sub-Poissonian behavior. There is a similarity between the energy main quantum number n and the absolute value of the complex variable z which labels the coherent states. This allows us to make a useful approximation in order to calculate the partition function and some thermodynamic characteristics of a canonical non interacting particle gas embedded in the infinite square quantum well.

Weak values and modular variables from a quantum phase-space perspective

We address two major conceptual developments introduced by Aharonov and collaborators through a \textit{quantum phase space} approach: the concept of \textit{modular variables} devised to explain the phenomena of quantum dynamical non-locality and the \textit{two-state formalism} for Quantum Mechanics which is a retrocausal time-symmetric interpretation of quantum physics which led to the discovery of \textit{weak values.} We propose that a quantum phase space structure underlies these profound physical insights in a unifying manner. For this, we briefly review the Weyl-Wigner and the coherent state formalisms as well as the inherent symplectic structures of quantum projective spaces in order to gain a deeper understanding of the weak value concept. We also review Schwinger's finite quantum kinematics so that we may apply this discrete formalism to understand Aharonov's modular variable concept in a different manner that has been proposed before in the literature. We discuss why we believe that this\ is indeed the correct kinematic framework for the modular variable concept and how this may shine some light on the physical distinction between quantum dynamical non-locality and the kinematic non-locality, generally associated with entangled quantum systems.

SELF-SIMILARITY PROPERTIES OF NAFIONIZED AND FILTERED WATER AND DEFORMED COHERENT STATES

By resorting to measurements of physically characterizing observables of water samples perturbed by the presence of Nafion and by iterative filtration processes, we discuss their scale free, self-similar fractal properties. By use of algebraic methods, the isomorphism is proved between such self-similarity features and the deformed coherent state formalism.

Coherent states formulation of polymer field theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.

Infrared Divergences in Light Front Field Theory and Coherent State Formalism

We discuss fermion self energy correction in light front QED using a coherent state basis. We show that if one uses coherent state basis instead of fock basis to calculate the transition matrix elements the true infrared divergences in $\delta m^2$ get canceled up to $O(e^4)$ . We show this in Light-front as well as in Feynman gauge.

On the number of soft quanta in classical field configurations

A crucial ingredient in the large-N quantum portrait of black holes proposed by Dvali and Gomez is the estimate of the number of soft quanta that make up the classical gravitational field. It is argued here that the coherent state formalism provides a way to calculate that number directly. As a consequence, the average energy of the soft quanta is such that the typical geometric size of the field source can be roughly interpreted as their de Broglie wavelength. The calculation is done for the electromagnetic field and for Newtonian gravity, and it is argued that the number of soft quanta should be unchanged in general relativity because of the long range nature of gravity.

Density Operator in Terms of Coherent States Representation with the Applications in the Quantum Information

In the quantum information theory operates with qubits and N-qubits that can be express through coherent states. Density operator admits a representation in terms of coherent states formalism. Consequently, in this paper the notions of qubit and density operators are described in the framework of coherent states. We have expressed a qubit as a coherent state, and thus a sequence of qubits becomes the tensor product of the coherent states. For the ensembles of qubits, it could be used the density operator, in order to describe the informational content of the ensemble. The coherent states representation may play an important role in the quantum information theory and the use of this formalism is not only theoretical, but also, due to its applications, of some practical relevance.