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A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy…
A new approach to cosmological perturbation theory has been recently introduced by Bartelmann et al., relying on nonequilibrium statistical theory of classical particles, and treating the gravitational interaction perturbatively. They…
We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges. Entanglement propagates with the walker. We apply this model to the case of a…
Based on the Lefschetz thimble formulation of path-integration, we analyze the (0+1) dimensional Thirring model at finite chemical potentials and perform hybrid Monte Carlo (HMC) simulations. We adopt the lattice action defined with the…
Recently a novel perturbative continuum limit for quantum gravity has been proposed and demonstrated to work at first order. Every interaction monomial $\sigma$ is dressed with a coefficient function $f^\sigma_\Lambda(\varphi)$ of the…
A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et…
A formula is proposed for continuing physical correlation functions to non-integer numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is…
Our main focus is to explore different models in noncommutative spaces in higher dimensions. We provide a procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables…
We discuss a general notion of quantum correlations in fermionic or bosonic indistinguishable particles. Our approach is mainly based on the identification of the algebra of single-particle observables, which allows us to devise an…
Weaver has recently defined the notion of a quantum relation on a von Neumann algebra. We demonstrate that the corresponding notion of a quantum function between two von Neumann algebras coincides with that of a normal unital…
First steps towards developing a new perturbation theory for molecular liquids are taken. By choosing a new form of splitting the site-site potential functions between molecules, we will get a set of atomic fluids as the reference system…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
The method of transfer functions is developed as a tool for studying Bell inequalities, alternative quantum theories and the associated physical properties of quantum systems. Non-negative probabilities for transfer functions result in…
We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and…
The explicit expressions for the one-loop non-perturbative corrections to the gravitational effective action induced by a scalar field on a stationary gravitational background are obtained both at zero and finite temperatures. The…
We formulate the finite-temperature perturbation theory of interacting scalar fields under external rotation. Because of the translational non-invariance in the radial direction, Green's functions are described using the Fourier-Bessel…
We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow…
We investigate varies correlation functions of modular Hamiltonians defined with respect to spatial regions in quantum field theories. These correlation functions are divergent in general. We extract finite correlators by removing divergent…
Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, we draw a conceptual parallel between two paradigms: the…