Heat bath coupling effects on interaction between Fröhlich vibration systems

The energy supplied to the Fröhlich vibration system in a living cell may condense in certain normal modes provided the coupling of the vibration system with a heat bath is nonlinear. The strong coupling of a coherent vibration system with a heat bath causes reduced energy condensation; high frequency modes are not excited and the energy condensed in the lowest frequency mode is smaller than the energy condensed in a system with weak coupling. The vibrations are polar and generate an electromagnetic field. The electromagnetic field mediates a long range interaction between the Fröhlich vibration systems; the interaction depends on the intensity of the generated electromagnetic field, and, therefore, on the energy condensed in the vibration system. The systems with strong coupling with a heat bath have weak interaction forces, which may be attractive as well as repulsive. The effect of coupling with a heat bath on interaction between the Fröhlich systems is a new contribution of this paper. The coherent vibration systems are assumed to be excited in protein molecules in cellular membranes. Protein phosphorylation may cause the strong Coulomb coupling of vibration systems with a heat bath and may have a fundamental effect on energy condensation.The work was supported, in part, by grant COST 244.     

Effect of changing incident wavelength on Raman features of optical phonons in SiC nanorods and TaC nanowires

Novel Raman scattering in polar semiconductor SiC and TaC one-dimensional materials have been carried out. With increasing incident laser wavelength from 488 to 633 nm there is a huge difference in Raman intensity enhancement for the LO/IF peaks and the TO peak. This has been interpreted as due to Fröhlich interaction and abundant defects in polar nano-scale semiconductor materials.     

Ground state features of the Fröhlich model

Following the ideas behind the Feynman approach, a variational wave function is proposed for the Fröhlich model. It is shown that it provides, for any value of the electron-phonon coupling constant, an estimate of the polaron ground state energy better than the Feynman method based on path integrals. The mean number of phonons, the average electronic kinetic and interaction energies, the ground state spectral weight and the electron-lattice correlation function are calculated and successfully compared with the best available results.Received: 2 July 2003, Published online: 19 November 2003PACS: 71.38.Fp Large or Fröhlich polarons     

Theory of the one-dimensional Peierls-Hubbard-model

We consider the properties of a one-dimensional Hamiltonian for electrons and phonons including the Fröhlich electron-phonon interaction as well as the Hubbard term for electron-electron interaction. The unperturbed band structure is of tight-binding form and half-filled.We derive the gap equation and the ground-state energy of the system in mean field approximation.We find antiferromagnetic ordering and lattice distortion and calculate the displacive and magnetic phase limits.D82 (Diss. TH Aachen)     

Computer simulation of the Fröhlich coherent vibrations

In a nonlinear vibration system with energy supply the lowest frequency mode may be coherently excited as was predicted by Fröhlich. Computer simulation of nonlinear vibration systems reveals that even the higher frequency modes may be excited. The conditions for higher frequency modes excitation are specified. Coherent states may be excited in the time period less than about one hour after switching on the energy supply.     

Electron-phonon interaction in hemispherical quantum dot

Within the framework of the dielectric continuum (DC) model, the optical phonon modes and electron-optical-phonon interaction in hemispherical quantum dot are investigated. The proper eigenfunctions for longitudinal optical (LO) and interface optical (IO) phonon modes are constructed. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron-phonon interaction. The dispersion relation of IO phonon modes is size independent. The potential applications of these results are also discussed.     

Exciton-phonon interaction in cylindrical semiconductor quantum dots

The exciton-longitudinal optical phonon interaction is theoretically investigated for the case of polar semiconductor cylindrical quantum dots embedded in semiconductor matrix. The theory is developed within the dielectric continuum model considering the Fröhlich interaction between electrons and confined bulk longitudinal optical phonons for a configurational interaction model of quantum dot. Representative longitudinal optical phonon mode for the exciton-phonon interaction is predicted for cylindrical InAs/GaAs quantum dots.     

Quantum mechanical coherence in human red blood cells

Fritz London predicted that the behavior of the quantum fluids ...might prove useful for an understanding of the macromolecular systems of biology which behave... much more simply than would be expected in view of the apparent great complexity of their structure. The Fröhlich theory is of an energy-driven laserlike process in living cells which should drive cellular phonons into coherence. Fröhlich's theory predicts specific ultra-long-range forces which can explain the presently mysterious, ordered tensor interactions within and without the living cell. Several different types of experiments demonstrate a specific ultralong-range interaction between mammalian red blood cells which accords with the postulates of the Fröhlich theory. One phenomenon seems to be compatible with processes analogous to self-focusing and trapping in nonlinear optics. As work progresses more and more biological mechanisms appear to be similar to those known in condensed matter physics.     

Thermal effect on the dielectric function and small polaron hopping conduction in organic molecular crystals

A Green function formalism is applied to study the dielectric function spectra and the small polaron hopping conduction in organic molecular crystals. In the calculations, the electron-phonon interaction is considered within the Hartree-Fock approximation, and the temperature effect is taken into account. Our theoretical approach is based on the polar electron-phonon interaction (Fröhlich type) to characterize the non-degenerate polaron gas, with the assumption of the electronic hopping between the first-neighbor.     

The Fröhlich kinetic equation with additional terms

The Fröhlich kinetic equation (FKE) describes the coherent excitation in a band of polarization waves consisting of normal modes. The FKE involves the one and two quanta terms representing energy supply, energy losses and energy channeling between the modes with the help of the heat bath. The energy channeling between the vibration systems located at different positions and the channeling connected with multiple quanta processes without the help of the heat bath are analyzed. The additional terms of the FKE are derived. The multiple quanta processes may channel the energy from the coherently excited mode (or modes) to higher frequency ones.     

Correlation length of the Peierls distortion

A Peierls distortion incommensurate with the lattice constant is considered in the Fröhlich model of a linear conductor. A prediction for the correlation length of the distortion is obtained using a Ginzburg-Landau expansion of the free energy for temperatures well belowT _p , the mean field Peierls transition temperature. The correlation length is found to be strongly increasing at aboutT _p /4.     

Theoretical evidence for the possible observation of relaxed excited states of Fröhlich polarons for polar crystals with α > 3.

The optical absorption spectrum of Fröhlich polarons has been calculated for the first time for arbitrary electron-phonon interaction     

Resonant long-range interactions between polar macromolecules

Motivated by its prospective biological relevance, the issue of resonant long-range interactions between two molecules displaying oscillating dipole moments is reinvestigated within the framework of classical electrodynamics. In particular, our findings shed new light on Fröhlich?s theory of selective long-range interactions between biomolecules. First, terms of a very long-range kind – which have never been reported so far – are found in the interaction potential, due to field retardation. Second, at variance with a long-standing belief, it is shown that sizable resonant long-range interactions may exist only if the interacting system is out of thermal equilibrium.     

Computer analysis of coherent electric vibrations in biological systems

The Fröhlich condensed state may be created in the system of vibration modes if the energy supply is above the critical one. A model of a vibration system of a limited number of modes in the frequency range 0·1–4 THz with uniform density of state function and limited energy in the condensed state (saturation) is used for computer simulation. Energy stored in particular modes is calculated as a function of energy supply and energy leakage to the heat bath. The energy stored in the condensed state may be greater than the thermal energy of the system. In the saturated condensed state the stored energy is independent of energy supply. In the vicinity of the critical energy supply the change of the supply of the order of 10% switches on or off the condensed state. The interaction between systems with condensed states leads to interaction forces. Dependent on various conditions these forces may be attractive or repulsive.     

Remark on the absence of absolutely continuous spectrum ford-dimensional Schrödinger operators with random potential for large disorder or low energy

We show that there is no absolutely continuous part in the spectrum of the Anderson tight-binding model for large disorder or low energy. The proof is based on the exponential decay of the Green's function proved by Fröhlich and Spencer. The extension of this result to the continuous case is also discussed.Laboratoire associé au CNRS- LA280     

First-order Raman scattering in cylindrical wurtzite nanowire

We have presented a theoretical study on electron resonant Raman scattering (ERRS) process associated with the bulk longitudinal optical (LO), surface optical (SO) and quasi-confined (QC) phonon modes in a free-standing wurtzite nanowire (NW). We consider the Fröhlich electron–phonon interaction in the framework of the dielectric continuum model. Numerical calculations on the GaN material reveal that differential cross-section (DCS) is sensitive to the wire size. The bulk LO and high-frequency quasi-confined (QC₊) phonons make main contributions to the DCS and the impact of the SO phonon can be negligible in the ERRS process. Moreover, scattering intensity of the bulk LO phonon is strongly enhanced as the incident photon energy approaches the energy band-gap of the GaN.     

Laboratory millimeter wave measurements of atmospheric aerosols

Measurements made in an untuned resonator by Fourier Transform Spectroscopy of atmospheric aerosols are explained by a pumped phonon model due to Fröhlich.     

Signatures of polaron formation in systems with local and non-local electron-phonon couplings

Polaron formation is investigated in a one-dimensional chain by taking into account both the local Holstein and the non-local SSH electron-phonon interactions. The study of the adiabatic regime points out that the combined effects of the two interactions are important mainly in the weak coupling regime. Thus, using the weak-coupling perturbation theory, spectral weights, effective masses, polaronic phase-diagram, and band structures are discussed. Contrarily to what happens in the Fröhlich and Holstein models, we find that the ratio between the coherent spectral weight and the mass renormalization ratio is greater than 1. Moreover, we show that the non-local electron-phonon interaction is responsible for the largest deviations of the band structure from the cosine shape of the free energy band.     

Formation of polaron clusters

The formation of spherical polaron clusters is studied within the Fröhlich polaron theory. In a dilute polaron gas, using the non-local statistical approach and the polaron pair interaction obtained within the Pekar strong coupling theory, the homogeneous phase results to be unstable toward the appearance of polaron clusters. The physical conditions of formation for the clusters are determined calculating the critical values of electron-phonon interaction for which bound states in the collective polaron potential develop. Finally the sequence in the filling of the states is found and the stability of the clusters is assessed.Received: 6 May 2004, Published online: 12 October 2004PACS: 71.38.-k Polarons and electron-phonon interactions