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V. M. Chabanov

Publications and source records attributed to V. M. Chabanov.

12 recordsLinked to original sources
arXiv2016

Electro-Optical Radiation of a Charged Particle in a Single Laser Beam Field

A peculiar radiation arising as a result of radiation interference of nonlinear oscillators excited by a monochromatic plane wave field of the incident particle is described. The radiation properties are determined by the fact that a phase of each oscillator radiation fields is synchronized by a wave field, while the radiation itself occurs due to the particle field influence on the oscillators. The consideration is performed for a thin film with negligible density effect. It is supposed that the contribution is given only by a long-wave part of the Weizsacker spectrum for which nonlinear polarization coefficients of medium are large.

physics.optics↗
arXiv2008

Single- and Multichannel Wave Bending

Recently, we have discovered a new concept of permanent wave resonance with potential spatial oscillations. This means the constant wave swinging frequency on the whole energy intervals of spectral forbidden zones destroying physical solutions and deepening the theory of waves in periodic potentials. It also shows the other side of strengthening the fundamentally important magic nuclear structures. A new language of wave bending will be presented to enrich our quantum intuition, e.g., the paradoxical effective attraction of barriers and repulsion of wells in multichannel systems.

quant-ph↗
arXiv2004

"Paradoxical" coexistence of continuum of 'bound' waves and discrete set of unlimited motion states

We have combined two remarkable phenomena: resonance tunneling and Anderson localization. It results in unexpected spectrum reverse to usual notions. It is demonstrated by the quantum system with chaotic distribution of potential resonance tunneling traps over the whole coordinate axis. The corresponding spectrum contains continuum of 'bound' states (Anderson's localization) and discrete tunneling resonances of unlimited wave propagation. It is in contrast to the usual situation with discrete bound and continuum of scattering states.

quant-ph↗
arXiv2004

Recovering the M-channel Sturm-Liouville operator from M+1 spectra

For a system of M coupled Schroedinger equations, the relationship is found between the vector-valued norming constants and M+1 spectra corresponding to the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The double set of norming vectors and associated spectrum of one of the M+1 boundary value problems uniquely specifies the matrix of potentials in the multichannel Schroedinger equation.

math-ph↗
arXiv2003

New theory of periodical systems by finite interval inverse problem

We show that the mechanism of gap formation has a resonance nature. The special real fundamental solutions were discovered which `paradoxically' have knot distribution with a period coinciding with that of potential at all energies of the whole lacuna interval. In terms of these solutions resonance gap appearance gets the most direct explanation: ever repeating hits by the potential result in exponential increase (decrease) of the wave amplitudes in the forbidden zones. The analogous alternating hits from opposite sides are responsible for the wave beatings in allowed zones. The inversion technique gives rise to zone control algorithms - shifting chosen boundaries of spectral bands, changing degree of zone forbiddenness. All this cannot be achieved by the previous Bloch theory.

quant-ph↗
arXiv2002

Toward the spectral zone control

The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to change the additional fundamental spectral parameter, the degree of exponential solution growth, at arbitrary given energy points inside the forbidden zones. This allows one to control tunneling through fragments of periodic structures at energies belonging to spectral gap. All the results are based on the finite interval inverse eigenvalue problem which provides us with complete sets of exactly solvable models. This is a radical extension (continuous ! multiplicity) in comparison to the famous finite-gap models.

quant-ph↗
arXiv2002

Obedient quantum mechanics: New status of the theory in the inverse problem approach

New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number, even complete sets of such models. So, the whole quantum mechanics is embraced by them. They correspond to all possible variations of spectral parameters which determine all properties of quantum systems. There appears a possibility to change at wish quantum objects by variation of these parameters as control levers and examine quantum systems in different thinkable situations. As a result, we acquire a vision of the intrinsic logic of behavior of any thinkable system, including real ones. The regularities revealed by computer visualization of these models were reformulated into unexpectedly simple universal rules of arbitrary transformations and what is more, their elementary constituents were discovered (new breakthrough). Of these elementary "bricks" it is possible in principle to construct objects with any given properties. This book of inverse problem quantum pictures is utmost intelligible and recommended to any physicists, chemists, mathematicians, biologists from students to professors who are interested in laws of the microworld.

quant-ph↗
arXiv2001

Universal Elementary Constituents of Potential Transformations Shifting Waves (Qualitative Theory)

It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization of a chosen bound state in a potential well of finite width are as well applicable to the scattering functions if states of the continuous spectrum are considered as bound states normalized to unity but distributed on an infinite interval with vanishing density. The potential perturbations of the same type on the half-axis concentrate the scattering wave at the origin, thus creating a bound state embedded into the continuous spectrum (zero width resonance). It is an improved version of paper: Annalen der Physik, 6 (1997) 136.

quant-ph↗
arXiv2001

Toward the Quantum Design of Multichannel Systems (The Inverse Problem Approach)

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 interaction matrices leading to the concentration of waves in a chosen partial channel and spatial localization are shown. The limiting instructive cases illustrating different phenomena which occur with the combination of 'incompatible' properties are considered. For example, the scattering solutions with different resonance widths at the same energy for the same interaction are revealed. Analogously, a 'paradoxical' coexistence of both strong reflection and absolute transparency is explained. The case of the violation of 'natural' asymptotic behavior of partial wave function is demonstrated : it has a greater damping decrement for the channel with a lower threshold. Peculiarities of the multichannel periodic structures, bound states embedded into continuum, resonance tunneling and degeneracy of states are described.

quant-ph↗
arXiv2000

Exact solutions for classical few-body systems from the multichannel quantum inverse problem

A surprising "duality" of the Newton equation with time-dependent forces and the stationary Schroedinger equation is discussed. Wide classes of exact solutions not known before for few-body Newton equations are generated directly from exactly solvable multichannel models discovered in quantum mechanics due to the inverse problem and the supersymmetry (SUSYQ) approach. The application of this duality to the control of the stability (bifurcations) of classical motions is suggested.

quant-ph↗
arXiv2000

On the Qualitative Theory of Non-Gamov Decay States

Complex potential transformations which add imaginary parts to chosen energy levels are given and qualitatively explained. Unexpected shape similarity of potential perturbations for real and imaginary E-shifts of bound states are exhibited. The imaginary E-shifts in the continuous spectrum lead to a surprising quasi-periodic field raking up initial propagating waves into localized states. Complex periodic potentials without lacunas (!) are constructed. The fission of quasi-bound states when neighbour complex eigenvalues approach one another is demonstrated. E-shift algorithms represent wide classes of exactly solvable quantum models for non-self-adjoint operators.

quant-ph↗