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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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  • A k-contact geometric approach to pseudo-gauge transformations
    We propose a starting point to the geometric description for the pseudo-gauge ambiguity in relativistic hydrodynamics, showing that it corresponds to the freedom to redefine the thermodynamic equilibrium state of the system. To do this, we develop for the first time a description of a relativistic hydrodynamic-like theory using k-contact geometry. In this approach, thermodynamic laws are encoded in a k-contact form, thermodynamical states are described via k-contact Legendrian submanifolds, which are analysed in detail, and conservation laws emerge as a consequence of Hamilton–de Donder–Weyl equations. The inherent non-uniqueness of these solutions is identified as the source of the pseudo-gauge freedom. We explicitly demonstrate how this redefinition of equilibrium works in a model of a Bjorken-like expansion, where a pseudo-gauge transformation is shown to leave the physical dissipation invariant.

  • Defining classical and quantum chaos through adiabatic transformations
    We present a unified formalism which identifies chaos in both quantum and classical systems in an equivalent manner by means of adiabatic transformations. The complexity of adiabatic transformations which preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations serves as a measure of chaos. This complexity is quantified by the (properly regularized) fidelity susceptibility or, more generally, by the geometric tensor. Physically this measure quantifies (i) long time instabilities of physical observables due to small changes in the Hamiltonian of the system and (ii) irregularity of physical observables contained in low frequency noise. Our exposition clearly showcases the common structures underlying quantum and classical chaos and allows us to distinguish integrable, chaotic but non-thermalizing, and ergodic/mixing regimes. We apply the fidelity susceptibility to a model of two coupled spins and demonstrate that it successfully predicts the universal onset of chaos, both for finite spin S and in the classical limit . Interestingly, we find that finite S effects are anomalously large close to integrability.

  • Vacuum electromagnetic field correlations between two moving points
    A renewed experimental interest in quantum vacuum fluctuations brings back the need to extend the study of electromagnetic vacuum correlations. Quantum or semi-classical models developed to understand various configurations should combine the effects of the zero-point fluctuations with those of blackbody radiation. In this paper, after a brief historical introduction and a rapid study of the electric field correlations in time domain, we propose exact and approximate expressions for the vacuum field correlations in Fourier space seen by moving points. We first present an exact computation of the electric field correlations, expressed in frequency space, between two points moving with opposite constant velocities on parallel trajectories. We also consider the electric field self-correlations, i.e. on the same moving point but at different frequencies, and comment the results related to special relativity. Then, we compute the exact main symmetrized quadratic electromagnetic field correlations between two points diametrically opposed on the same circular trajectory, with diameter r, covered at constant angular velocity Ω. We derive the expressions for the electromagnetic field correlations with itself and with its spatial derivatives, still at the locations of the moving points. Since the points we consider are accelerating, both the zero-point fluctuations and the blackbody spectrum give non-trivial results, for two-point correlations as well as for self-correlations. In both cases, results are shown at any vacuum temperature. For practical uses, we provide the first-order approximations in the small parameter with c being the speed of light.

  • Continuum model of isospectrally patterned lattices
    Isospectrally patterned lattices (IPLs) have recently been shown to exhibit a rich band structure comprising both regimes of localized as well as extended states. The localized states show a single center localization behavior with a characteristic localization length. We derive a continuum analog of the IPL which allows us to determine analytically its eigenvalue spectrum and eigenstates thereby obtaining an expression for the localization length which involves the ratio of the coupling among the cells of the lattice and the phase gradient across the lattice. This continuum model breaks chiral symmetry but still shows a pairing of partner states with positive and negative energies except for the ground state. We perform a corresponding symmetry analysis which illuminates the continuum models structure as compared to a corresponding chirally symmetric Hamiltonian.

  • Equivalence of mutually unbiased bases via orbits: general theory and a d = 4 case study
    In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases (ONBs) that are as ‘far apart’ as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct the space of its ONBs as a discrete quotient of the complete flag manifold. We introduce a metric on this space, which corresponds to the ‘MUBness’ distance. This allows us to describe equivalence between sets of MUBs in terms of the geometry of this space. The subspace of bases that are unbiased with respect to the standard basis decomposes into orbits under a certain group action, and this decomposition corresponds to the classification of complex Hadamard matrices. More generally, we consider a list of k MUBs, that one wishes to extend. The candidates are points in the subspace comprising all bases which are unbiased with respect to the entire list. This space also decomposes into orbits under a group action, and we prove that points in distinct orbits yield inequivalent MUB lists. Thus, we generalize the relation between complex Hadamard matrices and MUBs. As an application, we identify new symmetries that reduce the parameter space of MUB triples in dimension 4 by a factor of 4.