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Journal of Physics A: Mathematical and Theoretical - latest papers
Latest articles for Journal of Physics A: Mathematical and Theoretical
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Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature
We considered the vacuum polarization of a quantized charged scalar matter field in the background of a topological defect modeled by a finite-thickness tube with magnetic flux inside. The tube is impenetrable for quantum matter, and a generalized boundary condition of the Robin type is imposed at its surface. We have shown that in the flat space-time, the total induced vacuum energy does not depend on the coupling (ξ) of the scalar field’s interaction with the space-time curvature, only for the partial cases of the Dirichlet and Neumann boundary conditions on the tube’s edge. However, for generalized Robin boundary conditions, the total induced energy depends on the coupling ξ in flat space-time, at least for negative values of the boundary condition parameter .
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Exact Bethe quantum numbers of the massive XXZ chain in the two down-spin sector
Every solution of the Bethe ansatz equations (BAEs) is characterized by a set of quantum numbers called the Bethe quantum numbers, which are fundamental for evaluating each Bethe root numerically. We rigorously derive the Bethe quantum numbers for the real solutions of the spin-1/2 massive XXZ spin chain in the two down-spin sector, assuming the existence of solutions to some form of BAE. In the sector the quantum numbers J1 and J2 were derived for complex solutions, but not for real solutions. We show the exact results in the sector as follows. (i) When two Bethe quantum numbers are different, i.e. for , we introduce a graphical method, which we call a contour method, for deriving the solution of BAE to a given set of Bethe quantum numbers. By the method, we can readily show the existence and the uniqueness of the solution. (ii) When two Bethe quantum numbers are equal, i.e. for , we derive the criteria for the collapse of two-strings and the emergence of an extra two-string by an analytic method. (iii) We obtain the number of real solutions, which depends on the site number N and the XXZ anisotropy parameter ζ. (iv) We derive all infinite-valued solutions of BAE for the XXX spin chain in the two down-spin sector through the XXX limit. (v) We explicitly show the completeness of the Bethe ansatz in terms of the Bethe quantum numbers.
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Protecting cyclic controlled remote preparation of qudit states in a chain network
We concern on the cyclic controlled remote preparation of qudit states in a chain network. By choosing proper entanglement resources, we first propose a unidirectional scheme where single-qudit states can be deterministically prepared clockwise among multiple users. Each sender executes a positive operator-value measure under the elaborately constructed basis and a projective measurement (PM) under the generalized X basis, while the controller carries out a PM under the generalized Z basis. The corresponding receiver can restore the target state by executing recovery operations which is deduced by universal formulas. Then, we present a bidirectional scheme such that each sender can prepare two single-qudit states in both clockwise and counterclockwise directions. It is worth stressing that network coding is applied at the controller’s site to reduce the classical communication cost. The schemes are further extended to arbitrary multi-particle systems. Additionally, we consider the impact of amplitude damping noise and phase damping noise, and employ the strategy of weak measurement to counteract noise.
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Integrability and charge transport in asymmetric quantum-circuit geometries
We revisit the integrability of quantum circuits constructed from two-qubit unitary gates U that satisfy the Yang–Baxter equation. A brickwork arrangement of U typically corresponds to an integrable Trotterization of some Hamiltonian dynamics. Here, we consider more general circuit geometries which include circuits without any nontrivial space periodicity. We show that any time-periodic quantum circuit in which U is applied to each pair of neighbouring qubits exactly once per period remains integrable. We further generalize this framework to circuits with time-varying two-qubit gates. The spatial arrangement of gates in the integrable circuits considered herein can break the space-reflection symmetry even when U itself is symmetric. By analysing the dynamical spin susceptibility on ballistic hydrodynamic scale, we investigate how an asymmetric arrangement of gates affects the spin transport. While it induces nonzero higher odd moments in the dynamical spin susceptibility, the first moment, which corresponds to a drift in the spreading of correlations, remains zero. We explain this within a quasiparticle picture which suggests that a nonzero drift necessitates gates acting on distinct degrees of freedom. To the memory of Marko Medenjak, a dear friend and a brilliant colleague.
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Transmission resonances in scattering by δ ′ ...
We introduce a new exactly solvable model in quantum mechanics that describes the propagation of particles through a potential field created by regularly spaced -type point interactions, which model the localized dipoles often observed in crystal structures. We refer to the corresponding potentials as -combs, where the parameter θ represents the contrast of the resonant wave at zero energy and determines the interface conditions in the Hamiltonians. We explicitly calculate the scattering matrix for these systems and prove that the transmission probability exhibits sharp resonance peaks while rapidly decaying at other frequencies. Consequently, Hamiltonians with -comb potentials act as quantum filters, permitting tunneling only for specific wave frequencies. Furthermore, for each θ > 0, we construct a family of regularized Hamiltonians approximating the ideal model and prove that their transmission probabilities have a similar structure, thereby confirming the physical realizability of the band-pass filtering effect.