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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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  • Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions *
    The paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of a special averaging operator, which leads to a quasi-locality and is a natural generalization of a cutoff regularization in the coordinate representation in the case of a curved metric. It is proved that the regularization method is consistent with a process of gluing of manifolds and partition functions, that is, with the transition from submanifolds to the main manifold using an additional functional integration. It is shown that the method extends to other models, and is also consistent with the process of multiplicative renormalization. Additionally, we discuss issues related to the correct introduction of regularization and the locality.

  • Gradient projection method for constrained quantum control
    In this work, we adopt the gradient projection method (GPM) to problems of quantum control. For general N-level closed and open quantum systems, we derive the corresponding adjoint systems and gradients of the objective functionals and provide the projection versions of the Pontryagin maximum principle and the GPM, all directly in terms of quantum objects such as evolution operator, Hamiltonians, density matrices, etc. Various forms of the GPM, including one- and two-step, are provided and compared. We formulate the GPM both for closed and open quantum systems, latter for the general case with simultaneous coherent and incoherent controls. The GPM is designed to perform local gradient based optimization in the case when bounds are imposed on the controls. The main advantage of the method is that it allows to exactly satisfy the bounds, in difference to other approaches such as adding constraints as weight to an objective. We apply the GPM to several examples including generation of one- and two-qubit gates and two-qubit Bell and Werner states for models of superconducting qubits under the constraint when controls are zero at the initial and final times, steering an open quantum system to a target density matrix for simulating action of the Werner–Holevo channel, etc.

  • Spin chain techniques for angular momentum quasicharacters
    We study the ring of invariant functions over the N-fold Cartesian product of copies of the compact Lie group , modulo the action of conjugation by the diagonal subgroup, generalizing the group character ring. For N = 1, an orthonormal basis for the space of invariant functions is given by the irreducible characters, and the structure constants under pointwise multiplication are the coefficients of the Clebsch–Gordan series for the reduction of angular momentum tensor products (3j coefficients). For , the structure constants under pointwise multiplication of the corresponding invariants, which we term irreducible quasicharacters, are Racah recoupling coefficients, which can be decomposed as products of 9j coefficients (for N = 2, they are squares thereof). We identify the irreducible quasicharacters for with traces of representations of group elements, over totally coupled angular momentum states labelled by binary coupling trees T with N leaves, internal vertices and associated intermediate edge labels. Using concrete spin chain realizations and projection techniques, we give explicit constructions for some low degree and 4 quasicharacters. In the case N = 2, related methods are used to work out the expansions of products of generic, with elementary spin- , quasicharacters (equivalent to an ab initio evaluation of certain basic 9j coefficients). We provide an appendix which summarizes formal properties of the quasicharacter calculus known from our previous work for both and for compact G (Fuchs et al 2018 J. Math. Phys.59 083505 and Jarvis et al 2021 J. Math. Phys.62 033514). In particular, we provide an explicit derivation for the N = 2 angular momentum quasicharacter product rule.

  • Quantum correlations in a cluster spin model with three-spin interactions
    An exactly solvable cluster spin model with three-spin interaction couplings Jx(for XZX spin components) and Jy(for YZY spin components) in the presence of a transverse magnetic field h for a spin chain is investigated. For h = 0, and with only one non-zero interaction strength, the ground state is the cluster state. Through the Jordan–Wigner fermion mapping, the odd sites and the even sites form two separate transverse-XY chains, connected only through the boundary terms. Consequently, all measures of quantum correlations for nearest neighbour spins, the concurrence, the quantum mutual information and the quantum discord are all zero in the ground state. The dynamics is spin conserving for , exhibiting a line of critical points for , with an uncorrelated direct product ground state for . There are several quantum critical points in the parameter space, with multi-fold degenerate ground states. The magnetisation and the global entanglement measure exhibit strong singular features for the spin conserving case. The next-neighbour quantum correlation measures are investigated analytically, which exhibit singular features in the vicinity of degeneracy critical points. The Jy- and h- derivatives of the concurrence exhibit singular peak behaviour near the degeneracy critical points, except in the spin conserving case where the derivatives are zero.

  • Random non-Hermitian action theory for stochastic quantum dynamics: from canonical to path integral quantization
    We develop a theory of random non-Hermitian action that, after quantization, describes the stochastic nonlinear dynamics of quantum states in Hilbert space. Focusing on fermionic fields, we propose both canonical quantization and path integral quantization, demonstrating that these two approaches are equivalent. Using this formalism, we investigate the evolution of a single-particle Gaussian wave packet under the influence of non-Hermiticity and randomness. Our results show that specific types of non-Hermiticity lead to wave packet localization, while randomness affects the central position of the wave packet, causing the variance of its distribution to increase with the strength of the randomness.