Related papers: Multi-channel phase-equivalent transformation and …
A transformation of supersymmetric quantum mechanics for N coupled channels is presented, which allows the introduction of up to N degenerate bound states without altering the remaining spectrum of the Hamiltonian. Phase equivalence of the…
Understanding mixed-state quantum phases is a central challenge in the era of quantum simulation, where many existing studies focus on renormalization fixed points. In this work, we move beyond the renormalization fixed-point paradigm by…
Supersymmetric Quantum Mechanics may be used to construct reflectionless potentials and phase-equivalent potentials. The exactly solvable case of the $\lambda sech^2$ potential is used to show that for certain values of the strength…
We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits. We show that such circuits preserve topological degeneracy and the locality of all operators including both strong and weak…
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition…
We generalize eigen-phase preserving (EPP) supersymmetric (SUSY) transformations to $N>2$ channel Schr\"odinger equation with equal thresholds. It is established that EPP SUSY transformations exist only in the case of even number of…
The formalism developed in Refs.\cite{Guo:2023ecc,Guo:2024zal} that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the…
Supersymmetric (SUSY) transformations of the multi-channel Schr\"odinger equation with equal thresholds and arbitrary partial waves in all channels are studied. The structures of the transformation function and the superpotential are…
Two-dimensional Eliashberg equations have been solved by use of a mixed interaction with $s$- and $d$-channels. It is discussed what kind of pairing symmetry of the superconducting state can be realized when the channel mixing parameters…
Phase shifts for $\alpha$ + nucleon scattering generated by a multichannel RGM model of the five-nucleon system are subjected to iterative-perturbative ``mixed-case" inversion for energies below the reaction threshold. The resulting…
We investigate the localization properties of a quasi-one-dimensional two-channel system with symmetric and asymmetric onsite energies using the Aubry-Andr\'{e} model. By analyzing the Lyapunov exponent and localization length, we…
A method to calculate reactions in quantum mechanics is outlined. It is advantageous, in particular, in problems with many open channels of various nature i.e. when energy is not low. In the method there is no need to specify reaction…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
Quantum phase transitions encompass a variety of phenomena that occur in quantum systems exhibiting several possible symmetries. Traditionally, these transitions are explored by continuously varying a control parameter that connects two…
A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges…
We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. In the limit N >>1, where N is the number of states, we find that the survival probability of the initially…
A recent proposal of Sjoqvist et.al. to extend Pancharatnam's criterion for phase difference between two different pure states to the case of mixed states in quantum mechanics is analyzed and the existence of phase singularities in the…
We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the…
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a…
We show that it is possible to define shape-independent three-dimensional short-range quantum interactions in two parameter form for non-spherical angular momentum channels through double rescaling of potential strength. Unlike the special…