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Threshold Between Short and Long-range Potentials for Non-local Schrödinger Operators
We develop scattering theory for non-local Schrödinger operators defined by functions of the Laplacian that include its fractional power (−Δ) ρ with
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Sharp Spectral Inequalities for Fourth Order Differential Operators on Semi-Axis
In this paper we consider fourth order differential operators on semi-axis with Robin type boundary condition at zero. Using the commutation method...
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Lifshitz Tails for Quantum Waveguides with Random Boundary Conditions
In this study, we consider a quantum waveguide with random boundary conditions . Precisely we consider Laplace operator restricted to a two...
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Clustering Property of Quantum Markov Chain Associated to XY-model with Competing Ising Interactions on the Cayley Tree of Order Two
In the present paper we consider a Quantum Markov Chain (QMC) corresponding to the XY -model with competing Ising interactions on the Cayley tree of...
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Functional Central Limit Theorems and P(ϕ)1-Processes for the Relativistic and Non-Relativistic Nelson Models
We construct P ( ϕ ) 1 -processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and...
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Stability of the 2 + 2 Fermionic System with Point Interactions
We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via...
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Spectral Analysis of the 2 + 1 Fermionic Trimer with Contact Interactions
We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three...
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A Note on Time Operators
We construct a time operator of a self-adjoint operator H with finite dimensional CCR-domain. As corollaries, we show that there exists a time...
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On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree
It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers...
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Crystalline Conductance and Absolutely Continuous Spectrum of 1D Samples
We characterize the absolutely continuous spectrum of half-line one-dimensional Schrödinger operators in terms of the limiting behavior of the...
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Finite-size Energy of Non-interacting Fermi Gases
We study the asymptotics of the difference of the ground-state energies of two non-interacting N -particle Fermi gases in a finite volume of length L ...
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Bogolubov–Hartree–Fock Theory for Strongly Interacting Fermions in the Low Density Limit
We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials...
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Schnol’s Theorem and Spectral Properties of Massless Dirac Operators with Scalar Potentials
The spectra of massless Dirac operators are of essential interest, e.g., for the electronic properties of graphene, but fundamental questions such as...
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A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity
We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m , where each...
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Hardy Inequalities in Globally Twisted Waveguides
We establish various Hardy-type inequalities for the Dirichlet Laplacian in perturbed periodically twisted tubes of non-circular cross-sections. We...
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How Large is Large? Estimating the Critical Disorder for the Anderson Model
Complete localization is shown to hold for the d -dimensional Anderson model with uniformly distributed random potentials provided the disorder...