International Journal of Theoretical Physics最新文献

We accomplish the quantization of a few classical constrained systems á la (modified) Faddeev-Jackiw formalism. We analyze the constraint structure and obtain basic brackets of the theory. In addition, we disclose the gauge symmetries within the symplectic framework. We also provide an interpretation for Lagrange multipliers and outline a MATLAB implementation algorithm for symplectic formulation.

In this present paper we apply the Lie group theory associated fractional calculus to obtain the symmetries of the (zeta (t))-KdV fractional partial differential equation, which is given in terms of the (zeta (t))-Riemann-Liouville time fractional partial derivative, in which a particular case of the (zeta (t))-Hilfer fractional partial derivative is obtained. The calculus of symmetries consider the explicit formula of this infinitesimal extension of the fractional operator. The fractional partial equation is reduced to a fractional differential ordinary equation, and an analytical solution is proposed in the form of a power series. We obtain a nonlinear recurrence for the coefficients of the series. We discuss the linearized case for the fractional KdV equation, obtaining the Mainardi function as the solution, and the results are interpreted graphically. We then present the conservation law theorem for fractional (zeta (t)) operators, and we applied the law to find the law associated with each symmetry.

Coherence and magic (non-stabilizerness), as two different types of quantum resources playing fundamental roles in quantum information, have been widely studied separately. In this work, we reveal some intrinsic connections between them by characterizing and quantifying magic as the minimal coherence relative to the MUBs generated by the pure stabilizer states. This is motivated by the observation that in the stabilizer formalism of quantum computation, all pure stabilizer states in a prime-dimensional quantum system can be partitioned into (d+1) MUBs, and a pure state contains no magic if and only if it is incoherent relative to at least one of these (d+1) MUBs. We introduce quantifiers of magic via the minimal coherence relative to the (d+1) MUBs and compare them with some popular ones. Using the quantifiers of magic generated by the relative entropy of coherence and the (l_1)-norm of coherence, we evaluate the magic of some important states in low dimensional systems. Furthermore, we show the optimality of the quantum T-gates for generating magic resource in terms of our quantifiers of magic, which is consistent with previous results based on other quantifiers of magic.

In this study, we aim to derive exact analytical solutions, specifically bright soliton and singular solutions, for the pure-cubic nonlinear Schrödinger equation with third-order dispersion, incorporating cubic–quintic–septic nonlinearities, and to investigate its dynamic behavior through modulation instability analysis. This model, characterized by the dominance of third-order dispersion and the absence of the standard group-velocity dispersion term, accurately reflects realistic wave evolution in ultrafast optics and supercontinuum generation. The equation was analyzed using the new Kudryashov’s scheme, which is highly effective for solving high-order nonlinear Schrödinger-type equations. To complement this, a detailed modulation instability analysis was performed. As a result, bright soliton and singular solutions were successfully obtained. Furthermore, the conditions under which the model exhibits modulation instability were precisely identified. The findings were illustrated through 2D and 3D graphical representations. The primary novelty of this work lies in the successful application of the new Kudryashov method and the subsequent detailed modulation instability analysis to this particular, highly-nonlinear form of the Schrödinger equation. The derived analytical solutions serve as crucial benchmark data for future studies involving external perturbations.

This paper investigates the role of Gazeau-Klauder (GK) coherent states in quantum metrology, focusing on their application in enhancing measurement precision. We construct GK coherent states for exactly solvable systems, specifically the Pöschl-Teller potential and the Morse oscillator, and analyze their utility for displacement parameter estimation using quantum Fisher information as a metric. By comparing these states with standard coherent states of harmonic oscillator, we examine how their nonclassical properties influence the precision limits of quantum metrology. Furthermore, we explore the distinct effects of wave packet revivals and fractional revivals on the Fisher information, demonstrating that these dynamical phenomena can periodically generate significant gains in measurement sensitivity. Our analysis contributes to understanding how the inherent nonclassicality of generalized coherent states, tailored by the system’s potential, can be used to surpass classical limits, with potential applications in advanced measurement technologies.

A recent study employing Fourier transform techniques presents an incomplete treatment of the Hyers–Ulam stability of linear differential equations with constant coefficients, particularly in the context of the second-order undamped harmonic oscillator (i.e., the spring-mass system). That paper asserts that such systems are universally Hyers–Ulam stable. This paper aims to clarify that the Hyers–Ulam stability of these equations is, in fact, more nuanced and critically dependent on system parameters such as the mass, damping coefficient, and spring constant. Specifically, the undamped spring–mass system is Hyers–Ulam unstable when the mass and spring constant are both positive or both negative. This instability arises due to resonance phenomena in the perturbed system. We also discuss and illustrate additional instability cases to provide a more complete stability analysis.

Based on quantum multi-hop networks, a general scheme is designed for remote implementation of quantum operations. Firstly, different types of GHZ states are shared in advance along the quantum path. Subsequently, by employing bidirectional quantum teleportation, finite state machines are constructed to determine the recovery operations at both the source and destination nodes. Furthermore, in comparison with existing similar schemes, the proposed approach achieves a reduction in classical communication cost by approximately 25% as the number of hops increases.

A variational framework is developed here to quantize fermionic fields based on the extended stationary action principle. From the first principle, we successfully derive the well-known Floreanini-Jackiw representation of the Schrödinger equation for the wave functional of fermionic fields - an equation typically introduced as a postulate in standard canonical quantization. The derivation is accomplished through three key contributions. At the conceptual level, the classical stationary action principle is augmented to include a correction term based on the relative entropy arising from field fluctuations. Then, an extended canonical transformation for fermionic fields is formulated that leads to the quantum version of the Hamilton-Jacobi equation in a form consistent with the Floreanini-Jackiw representation; Third, necessary functional calculus with Grassmann-valued field variables is developed for the variation procedure. The quantized Hamiltonian can generate the Poincaré algebra, thus satisfying the symmetry requirements of special relativity. Concrete calculation of the probability of particle creation for the fermionic field under the influence of constant external field confirms that the results agree with those using standard canonical quantization. We also show that the framework can be applied to develop theories of interaction between fermionic fields and other external fields such as electromagnetic fields, non-Abelian gauge fields, or another fermionic field. These results further establish that the present variational framework is a novel alternative to derive quantum field theories.

We present an example that the usual natural extension of a generalized effect algebra to an effect algebra need not preserve infinite suprema, i.e., the original generalized effect algebra need not be a ((sigma )-)complete order ideal in the extension.