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Authors:Oğul Esen; Ayten Gezici Hasan Gümral First page: 365201 Abstract: We present the locally conformal generalization of the Euler–Lagrange equations. We determine the dual space of the LCS Hamiltonian vector fields. Within this dual space, we formulate the Lie–Poisson equation that governs the kinetic motion of Hamiltonian systems in the context of local conformality. By expressing the Lie–Poisson dynamics in terms of density functions, we derive locally conformal Vlasov dynamics. In addition, we outline a geometric pathway that connects LCS Hamiltonian particle motion to locally conformal kinetic motion. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-21T23:00:00Z DOI: 10.1088/1751-8121/ad6cb7 Issue No:Vol. 57, No. 36 (2024)

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Authors:Pablo Fernández; Miguel A Martin-Delgado First page: 365301 Abstract: We introduce a class of circuits that solve a particular case of the Bernstein–Vazirani recursive problem for second-level recursion. This class of circuits allows for the implementation of the oracle using a number of T-gates that grows linearly with the number of qubits in the problem. We find an application of this scheme to quantum homomorphic encryption (QHE), which is an important cryptographic technology useful for delegated quantum computing, allowing a remote server to perform quantum computations on encrypted quantum data, so that the server cannot know anything about the client’s data. Liang’s QHE schemes are suitable for circuits with a polynomial number of gates . Thus, the simplified circuits we have constructed can be evaluated homomorphically in an efficient manner. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-21T23:00:00Z DOI: 10.1088/1751-8121/ad6c04 Issue No:Vol. 57, No. 36 (2024)

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Authors:Yuta Sakamoto; Takahiro Sakaue First page: 355002 Abstract: Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from that in a finite interval with two absorbing boundaries. Here, we propose a method, which we refer to as a method of filtration, that allows us to construct the latter from only the knowledge of the former. We demonstrate that our method yields two solution forms, a method of eigenfunction expansion-like form and a method of image-like form. In particular, we argue that the latter solution form is a generalization of the method of image applicable to a stochastic process for which the method of image generally does not work, e.g. the Ornstein–Uhlenbeck process. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-20T23:00:00Z DOI: 10.1088/1751-8121/ad6ab7 Issue No:Vol. 57, No. 35 (2024)

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Authors:Hua Li; Yong Xu, Ralf Metzler Jianwei Shen First page: 355201 Abstract: Transitions between long-lived states are rare but important. The statistic of successful transitions is considered in transition path theory. We here consider the transition path properties of a generalized Langevin equation with built-in memory. The general form of the approximate theoretical solutions to the transition path time distribution, mean transition path time, and coefficient of variation are obtained from the generalized Smoluchowski equation. Then, the accuracy of our theoretical results is verified by the Forward Fluxing Sampling scheme. Finally, two examples are worked out in detail. We quantify how the potential function and the memory parameters affect the transition path properties. The short time limit of transition path time distribution always has an exponential decay. For the parabolic potential case, the memory strongly affects the long-time behavior of the transition path time distribution. Our results show that the behavior of the mean transition path time is dominated by the smaller of the two memory times when both memory times exceed the intrinsic diffusion time. Interestingly, the results also show that the memory can effect a coefficient of variation of transition path times exceeding unity, in contrast to Markovian case. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-20T23:00:00Z DOI: 10.1088/1751-8121/ad6db1 Issue No:Vol. 57, No. 35 (2024)

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Authors:Andy Manapany; Sébastien Fumeron Malte Henkel First page: 355202 Abstract: The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection–diffusion equation is also solved and an application to Pennes bioheat model is presented. Generically, a wave-like transport at short times passes over to a diffusion-like behaviour at later times. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-20T23:00:00Z DOI: 10.1088/1751-8121/ad6c02 Issue No:Vol. 57, No. 35 (2024)

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Authors:M Avendaño-Camacho; J C Ruíz-Pantaleón Yu Vorobiev First page: 355203 Abstract: In the context of averaging method, we describe a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups on fibered phase spaces. Some symmetry properties of Wong’s type equations are derived from the main results. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-20T23:00:00Z DOI: 10.1088/1751-8121/ad6c00 Issue No:Vol. 57, No. 35 (2024)

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Authors:L Salasnich; M G Pelizzo F Lorenzi First page: 355302 Abstract: We provide a thermodynamic derivation of the only-phase Popov action functional, which is often adopted to study the low-energy effective hydrodynamics of a generic nonrelativistic superfluid. It is shown that the crucial assumption is the use of the saddle point approximation after neglecting the quantum-pressure term. As an application, we analyze charged superfluids (superconductors) coupled to the electromagnetic field at zero temperature. Our only-phase and minimally-coupled theory predicts the decay of the electrostatic field inside a superconductor with a characteristic length much smaller than the London penetration depth of the static magnetic field. This result is confirmed also by a relativistic only-phase Popov action we obtain from the Klein–Gordon Lagrangian. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-13T23:00:00Z DOI: 10.1088/1751-8121/ad6ab3 Issue No:Vol. 57, No. 35 (2024)

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Authors:David Raveh; Rafael I Nepomechie First page: 355303 Abstract: Bethe equations, whose solutions determine exact eigenvalues and eigenstates of corresponding integrable Hamiltonians, are generally hard to solve. We implement a Variational Quantum Eigensolver approach to estimating Bethe roots of the spin-1/2 XXZ quantum spin chain, by using Bethe states as trial states, and treating Bethe roots as variational parameters. In numerical simulations of systems of size up to 6, we obtain estimates for Bethe roots corresponding to both ground states and excited states with up to 5 down-spins, for both the closed and open XXZ chains. This approach is not limited to real Bethe roots. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-19T23:00:00Z DOI: 10.1088/1751-8121/ad6db2 Issue No:Vol. 57, No. 35 (2024)

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Authors:Marc Mars; Raül Vera First page: 355402 Abstract: Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-13T23:00:00Z DOI: 10.1088/1751-8121/ad6ab6 Issue No:Vol. 57, No. 35 (2024)

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Authors:Mark Aleksiejuk; David A Burton First page: 355701 Abstract: A relativistic non-linear scalar field theory is developed from a 2+2-dimensional decomposition of the cold plasma field equations, and the theory is used to investigate a 1+1-dimensional description of a laser wakefield accelerator. The relationship between the properties of a compact laser pulse and its wake is explored. Non-linear solutions are sought describing a regular (i.e. unbroken) wake driven by a prescribed rectangular circularly-polarised laser pulse. An upper bound on the dimensionless amplitude a0 of the laser pulse is determined as a function of the phase speed v of the wake. The asymptotic behaviour of the upper bound on a0 as is shown to agree with well-established, but approximate, results obtained using the conventional encoding of the plasma degrees of freedom. Our approach leads to a closed-form expression for the upper bound on a0 which is exact for all values of the phase speed of the wake, unlike conventional results that are applicable only when v is sufficiently close to c. Citation: Journal of Physics A: Mathematical and Theoretical PubDate: 2024-08-19T23:00:00Z DOI: 10.1088/1751-8121/ad6db0 Issue No:Vol. 57, No. 35 (2024)