A new hierarchy of upper and lower bounds on expectation values

Upper and lower bounds are constructe for expectation values of functions of a real random variable with derivatives up to orderN+1 which are alternately negative and positive over the whole range of interest. The bounds are given by quadrature formulas with weights and abscissas determined by the firstN+1 moments of the underlying probability distribution. Application to a simple disordered phonon system yields sharp bounds on the specific heat.     

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio. Collective features of phonon current cumulants are also revealed.     

Relaxation and 1/f noise in phonon systems

This paper examines the relationships that exist between low-frequency fluctuations of the rate of dissipation in nonequilibrium thermodynamic systems and higher-order multitime statistical moments of equilibrium noise. In particular, it studies the relationships between internal friction fluctuations in the phonon system being excited and low-frequency fluctuations of Raman scattering of light in an equilibrium phonon system. We show that both processes are related to strong fluctuations in the phase diffusion rate and the relaxation of phonon modes generated, in turn, by the exponential instability of the dynamical paths of the system. Zh. éksp. Teor. Fiz. 111, 2086–2098 (June 1997)     

Indirect RKKY interaction in doped armchair nanotube due to electron phonon interaction effects

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in doped armchair nanotube in the presence of gap parameter. The effects of both next nearest neighbor hopping parameter and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments have been analyzed. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the transverse static spin susceptibility of armchair graphene nanoribbon in the presence of electron-phonon coupling and gap parameter. The spin susceptibility components are calculated using Green’s function approach for Holstein model Hamiltonian. The effects of electron doping on dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of next nearest neighbor hopping parameter on the spatial behavior of RKKY interactions are different in the presence of electron phonon coupling.     

Lattice dynamics of BaClF and SrClF

The lattice dynamics of tetragonal BaClF and SrClF have been worked out in detail on the basis of a shell model. The shell model parameters obtained from the transfer of corresponding parameters from the respective fluorides gives rise to long wavelength optic phonons in good agreement with the experimental results. Calculations have been made of the phonon dispersion relations, elastic constants, phonon density of states, temperature variation of specific heats and the lattice phonon moments.The mean square displacements of the various ions in these systems have also been computed over a wide range of temperature. Comparison with the available X-ray experimental data on thermal vibration parameters shows the agreement to be satisfactory.     

Nonergodicity and dynamical approach to the anharmonic oscillator

General lower bounds for the time average C^AA(∞)≡lim_T→∞(1/T)∝^T₀ C^AA(t) dt of the correlation C^AA(t)≡A(t)A(0)−A² of an arbitrary variable A are derived, which depend only on the temperature derivatives of the canonical averages of A and the Hamiltonian of the system. The bounds may be used to give good estimations for C^AA(∞) which is different from zero when A is nonergodic. It is important to take care of these terms when dynamical theories made for interacting systems are applied to isolated systems. We show explicitely that our recently developed dynamical approach to phonon systems with quartic anharmonicity yields excellent results for the corresponding isolated system, the anharmonic single well oscillator, when nonvanishing time averages are taken into account.     

Testing the Equivalence Principle in the Quantum Regime

We consider possible tests of the Einstein Equivalence Principle for physical systems in which quantum-mechanical vacuum energies cannot be neglected. Specific tests include a search for the manifestation of non-metric effects in Lamb-shift transitions of hydrogenic atoms and in anomalous magnetic moments of massive leptons. We discuss how current experiments already set bounds on the violation of the equivalence principle in this sector and how new (high-precision) measurements of these quantities could provide further information to this end.     

On improvable bounds for polaron systems in an external potential

A variational approach is proposed that allows one to obtain in a regular way a sequence of improvable upper bounds for the ground-state energy of various polaron models confined in an external electrostatic potential. The proposed approach can be used for an arbitrary electron–phonon interaction constant and allows generalization to the case of polaron-type systems in a constant external magnetic field.     

Moments of the phonon spectrum in lithium and rubidium halides from specific heat data

The moments of the phonon spectrum in lithium and rubidium halides are estimated from the experimental specific heat data and they are compared with the theoretically calculated moments using the shell model of lattice dynamics.     

Lower bounds for the electric susceptibility

New lower bounds for the susceptibility in terms of the first and second moments are derived. These lower bounds are applied in the problem of the electric susceptibility.     

Localization Bounds for Multiparticle Systems

We consider the spectral and dynamical properties of quantum systems of n particles on the lattice \({\mathbb{Z}^d}\) , of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the lattice sites and a finite-range interaction. Two basic parameters of the model are the strength of the disorder and the strength of the interparticle interaction. It is established here that for all n there are regimes of high disorder, and/or weak enough interactions, for which the system exhibits spectral and dynamical localization. The localization is expressed through bounds on the transition amplitudes, which are uniform in time and decay exponentially in the Hausdorff distance in the configuration space. The results are derived through the analysis of fractional moments of the n-particle Green function, and related bounds on the eigenfunction correlators.     

Anharmonic phonons and structural phase transitions

Exact results for the order parameter and the meansquare displacement as functions of temperature are given for a quantum interacting phonon Hamiltonian with quartic anharmonicities. Upper bounds for the transition temperature are also derived. Approximate theories including the mean field approximation, the random phase approximation (or quasiharmonic approximation) and the self consistent approach (using Blume-Hubbard scheme) are compared with our exact results. The mean field approximation for the meansquare displacement is found to violate our bounds.The classical value is shown to form a lower bound for the kinetic energy. Upper bounds for the kinetic energy are obtained showing the region of temperature in which the use of the high temperature expansion of the fluctuation-dissipation theorem is justified. Comparison of the Hamiltonian and our results with electron-paramagnetic-resonance measurements are discussed.     

Ab initio calculations of magnetic structure and lattice dynamics of Fe/Pt multilayers

The magnetization distribution, its energetic characterization by the interlayer coupling constants and lattice dynamics of (001)-oriented Fe/Pt multilayers are investigated using density functional theory combined with the direct method to determine phonon frequencies. It is found that ferromagnetic order between consecutive Fe layers is favoured, with the enhanced magnetic moments at the interface. The bilinear and biquadratic coupling coefficients between Fe layers are shown to saturate fast with increasing thickness of nonmagnetic Pt layers which separate them. The phonon calculations demonstrate a rather strong dependence of partial iron phonon densities of states on the actual position of Fe monolayer in the multilayer structure.     

Topological Phonon Modes in a Two-Dimensional Wigner Crystal

We investigate the spin-orbit coupling effect in a two-dimensional(2D)Wigner crystal.It is shown that sufficiently strong spin-orbit coupling and an appropriate sign of g-factor could transform the Wigner crystal to a topological phonon system.We demonstrate the existence of chiral phonon edge modes in finite size samples,as well as the robustness of the modes in the topological phase.We explore the possibility of realizing the topological phonon system in 2D Wigner crystals confined in semiconductor quantum wells/heterostructure.It is found that the spin-orbit coupling is too weak for driving a topological phase transition in these systems.It is argued that one may look for topological phonon systems in correlated Wigner crystals with emergent effective spin-orbit coupling.     

Carbon nanotube ballistic thermal conductance and its limits

Calculations of the quantum-mechanical ballistic thermal conductance of single-walled carbon nanotubes, graphene, and graphite are presented, which explain previous experimental results, and directly disprove earlier theoretical calculations. The ballistic thermal conductances are smaller than had been previously thought, whereas the maximum sample lengths in which phonon transport remains ballistic are orders of magnitude larger than previously suggested. Good agreement with previous experiments is obtained, which shows that measured lower bounds to the thermal conductance of multiwalled carbon nanotubes are very close to the upper theoretical bounds for graphite. The bounds shown here draw a line between what is physical and unphysical in any measurements or calculations of carbon nanotube thermal conductance, and constitute a necessary test to their validity.     

Local density of states in a disordered chain: A renormalization group approach

We apply renormalization group techiques to evaluate the local density of phonon states for the isotopically (randomly) disordered linear chain. The method is based on a systematic decimation of atoms in the chain. Numerical studies reveal a richly structured spectrum, in reasonable agreement both with numerical simulations and with exact moments results. This is the first analytic alloy approximation which takes into account potential fluctuations of arbitrary range.     

On Nonlinear Functionals of Random Spherical Eigenfunctions

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.     

The effects of electron–phonon interaction on anisotropic RKKY interaction in graphene nanoribbon

We study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in doped armchair graphene nanoribbon. The effects of both external magnetic field and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain both transverse and longitudinal static spin susceptibilities of armchair graphene nanoribbon in the presence of electron-phonon coupling and magnetic field. The spin susceptibility components are calculated using the spin dependent Green’s function approach for Holstein model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of magnetic field on the spatial behavior of in-plane and longitudinal RKKY interactions are different in the presence of magnetic field.     

Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.     

Photon-Assisted Heat Generation by Electric Current in a Quantum Dot Attached to Ferromagnetic Leads

Heat generated by electric current in a quantum dot device contacting a phonon bath is studied using the nonequilibrium Green function technique.Spin-polarized current is generated owing to the Zeeman splitting of the dot level.The current's strength and the spin polarization are further manipulated by changing the frequency of an applied photon field and the ferromagnetism on the leads.We find that the associated heat by this spinpolarized current emerges even if the bias voltage is smaller than the phonon energy quanta and obvious negative differential of the heat generation develops when the photon frequency exceeds that of the phonon.It is also found that both the strength and the resonant peaks' position of the heat generation can be tuned by changing the value and the arrangement configurations of the magnetic moments of the two leads,and then provides an effective method to generate large spin-polarized current with weak heat.Such a result may be useful in designing low energy consumption spintronic devices.