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We investigate the quantum dynamics of neutral atoms subject to a uniform spin-dependent gauge field. In particular, we analyze a simple experimental scheme to generate the Landau quantization in a two dimensional atomic gas with internal…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
We discuss a simple procedure for computing one-loop quantum energies of any static field configuration that depends non-trivially on only a single spatial coordinate. We specifically focus on domain wall-type field configurations that…
We investigate the quantum thermodynamical properties of localised relativistic quantum fields, and how they can be used as quantum thermal machines. We study the efficiency and power of energy transfer between the classical gravitational…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
It has been found, that free electromagnetic (EM) field in restricted volume (typical experimental case) consists of two independent and equally possible components with different parity under spatial inversion transformations. Either of…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with…
We suggest to use the action-angle variables for the study of properties of (quasi)particles in quantum rings. For this purpose we present the action-angle variables for three two-dimensional singular oscillator systems. The first one is…
Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations…
Theory of the quantum quartic oscillator is developed with close attention to the energy cutoff one needs to impose on the system in order to approximate the smallest eigenvalues and corresponding eigenstates of its Hamiltonian by…
The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave…
We present a semidefinite program (SDP) algorithm to find eigenvalues of Schr\"{o}dinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the…
Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…
The variational quantum eigensolver (VQE) has emerged as one of the leading quantum algorithms for solving electronic structure problems on near-term noisy intermediate-scale quantum devices. However, its practical application to quantum…
In the present report, a set of theoretical results obtained in the period from 1991 to 2005 are reviewed. The physical systems under study include quark models of hadrons, inert atom clusters, atomic traps, and electrons and excitons…