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arXiv:1510.01279 · Canadian Journal of Physics

On formation of long-living states

Boris I. Ivlev

Published Aug 28, 2016• 2 citations
arXivHTMLPDF

Abstract

The motion of a particle in a potential well is studied when the particle is attached to an infinite elastic string. This is generic with the problem of dissipative quantum mechanics investigated by Caldeira and Leggett (Ann. Phys. 149, 374 (1983). doi: 10.1016/0003-4916(83)90202-6 ). Besides the dissipative motion there is another scenario of interaction of the string with the particle attached. Stationary particle–string states exist with string deformations accompanying the particle. This is like polaronic states in solids. Our polaronic states in the well are non-decaying and have a continuous energy spectrum. These states may have a link to quantum electrodynamics.

DOI
10.1139/cjp-2016-0227

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The motion of a particle in a potential well is studied when the particle is attached to an infinite elastic string. This is generic with the problem of dissipative quantum mechanics investigated by Caldeira and Leggett (Ann. Phys. 149, 374 (1983). doi: 10.1016/0003-4916(83)90202-6 ). Besides the dissipative motion there is another scenario of interaction of the string with the particle attached. Stationary particle–string states exist with string deformations accompanying the particle. This is like polaronic states in solids. Our polaronic states in the well are non-decaying and have a continuous energy spectrum. These states may have a link to quantum electrodynamics.
We use a strain description to couple long-range elastic fields adiabatically to electronic density to describe the behavior of a quantum particle in an elastic medium. We show that in this generalization of the Holstein polaron problem, a bound polaronic state results with strong long-range angular dependence in the elastic fields, but a localized electronic core. The deformation of the elastic fields creates an anisotropic, indirect interaction between polarons extending to large distances. For a given density of polarons, this interaction favors the formation of strings of polarons in preferred directions.
The real-time dynamics of a quantum-mechanical particle in a dissipative double-well potential at finite temperatures is solved ab initio by means of a multisite spin-hopping analysis. Both the macroscopic-quantum-coherence and macroscopic-quantum-tunneling regimes are covered. The theory gives a unified picture of tunneling transport and vibrational relaxation. The analysis is based on the Ohmic-model Hamiltonian [A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983); R. Zwanzig, J. Stat. Phys. 9, 215 (1973)] or the equivalent ``particle-on-a-string'' model [H. Dekker, Phys. Rev. A 31, 1067 (1985)]. The reduced quantum Liouville equation for the particle is derived and written in the energy representation. The usual truncation to the ground-state doublet of the vibrational ladder is not made. The interdoublet vibrational dynamics considerably simplifies upon coarse-graining and in the harmonic-well approximation. The intradoublet pseudospin dynamics is treated in the ``noninteracting-blip approximation'' [A. J. Leggett et al., Rev. Mod. Phys. 59, 1 (1987)]. The coarse-grained vibrational processes give rise to a Markovian one-step spin hopping between adjacent doublets (or sites). Inter alia ``inhomogeneous broadening'' and ``motional narrowing'' [P. E. Parris and R. Silbey, J. Chem. Phys. 83, 5619 (1985)] are discussed as special cases.
With the use of Hartree-Fock method we find that in narrow band solids there may arise an electron phase separation. These electron regions are spontaneously self-organized into the form of linear electron strings or droplets. The many-body self-trapping effect is due to a deformational electron-phonon interaction. A single string in a narrow band solid consists of a continuos chain of atoms which have trapped electrons (holes) due to the self-creation of a deformation well around this chain. We find that the length of such strings depends on the constant of deformation potential, the elastic modulus of the crystal and the inter-site Coulomb interaction between the particles.