Related papers: Reducible boundary conditions in coupled channels
Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly…
In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found.…
An approach to bound states based on unitary transformations of Hamiltonians is presented. The method is applied to study the interaction between electrons in a BCS $s$-wave superconductor and a quantum spin. It is shown that known results…
In this paper, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by…
We apply a boost-invariant similarity renormalization group procedure to a light-front Hamiltonian of a scalar field phi of bare mass mu and interaction term g phi^3 in 6 dimensions using 3rd order perturbative expansion in powers of the…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the "star-genvalue" equation and to the time evolution equation. These…
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…
Using renormalization group techniques, we study spectral and transport properties of a spinless interacting quantum dot consisting of two levels coupled to metallic reservoirs. For strong Coulomb repulsion $U$ and an applied Aharonov-Bohm…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…
We study Hamiltonian systems with point interactions and give a systematic description of the corresponding boundary conditions and the spectrum properties for self-adjoint, PT-symmetric systems and systems with real spectra. The…
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by showing that approximate symmetry operators---unitary operators whose commutators with the Hamiltonian…
In dimension $d=1,2,3$ we define a family of two-channel Hamiltonians obtained as point perturbations of the generator of the free decoupled dynamics. Within the family we choose two Hamiltonians, $\hat H_0$ and $\hat H_\ve$, giving rise…
We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above…
We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem,…
This paper shows that the resolvent algebra $\mathcal{R}\left( \mathbb{R}^2,\sigma \right)$ can accommodate dynamics induced by self-adjoint Hamiltonians on $L^2\left( \mathbb{R} \right)$ describing a single non-relativistic spinless…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
Contact reduction is very closely related to symplectic reduction, but it allows symmetries that are not manifest in Hamiltonian mechanics and moreover, solution of the reduced problems yields solution of the original problem without…
We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem…
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable…