MULTISCALE BORN-OPPENHEIMER THEORY OF COLLECTIVE ELECTRON-NUCLEAR DYNAMICS IN NANOSYSTEMS

2011 ◽  
Vol 10 (05) ◽  
pp. 605-614 ◽  
Author(s):  
ZEINA SHREIF ◽  
PETER ORTOLEVA
Keyword(s):  
Multiscale Analysis ◽  
Mean Field Theory ◽  
Mean Field ◽  
Coarse Grained ◽  
Electron Dynamics ◽  
Mass Ratio ◽  
Many Body ◽  
Nuclear Mass ◽  
Nuclear Dynamics ◽  
Scale Ratio

Born-Oppenheimer theory is based on the separation in timescales between the nuclear and electron dynamics implied by the electron-to-nuclear mass ratio. This makes it naturally fit into a multiscale analysis. It is shown that a fully dynamical Born-Oppenheimer theory follows from a multiscale ansatz on the wave function and a Taylor expansion in the mass ratio. Allowing for a larger spatial scale of electron motion yields an understanding of boson, fermion, and more complex excitations that involve quasi-particles with an effective mass not equal to that of the electron. The theory involves a unified asymptotic expansion in a mass and length scale ratio, and preserves all many-body effects via accounting for the full strength of the interparticle forces. A novel mean-field theory emerges based on the fact that long-scale migration allows each electron to interact with many others on the space-time scale relevant to the coarse-grained equation. Implications for computational methods and applications to quantum nanosystems such as quantum dots, nanowires, superconducting nanoparticles, and liquid He droplets are discussed.

ON STRONGLY NONLINEAR AUTOREGRESSIVE MODELS: IMPLICATIONS FOR THE THEORY OF TRANSIENT AND STATIONARY RESPONSES OF MANY-BODY SYSTEMS

2013 ◽  
Vol 12 (04) ◽  
pp. 1350022 ◽  
Author(s):  
T. D. FRANK ◽  
S. MONGKOLSAKULVONG
Keyword(s):  
Evolution Equations ◽  
Mean Field Theory ◽  
Mean Field ◽  
Ar Model ◽  
Many Body ◽  
Response Dynamics ◽  
Process Mean ◽  
Stationary Response ◽  
Strongly Nonlinear ◽  
Many Body Systems

Two widely used concepts in physics and the life sciences are combined: mean field theory and time-discrete time series modeling. They are merged within the framework of strongly nonlinear stochastic processes, which are processes whose stochastic evolution equations depend self-consistently on process expectation values. Explicitly, a generalized autoregressive (AR) model is presented for an AR process that depends on its process mean value. Criteria for stationarity are derived. The transient dynamics in terms of the relaxation of the first moment and the stationary response to fluctuations in terms of the autocorrelation function are discussed. It is shown that due to the stochastic feedback via the process mean, transient and stationary responses may exhibit qualitatively different temporal patterns. That is, the model offers a time-discrete description of many-body systems that in certain parameter domains feature qualitatively different transient and stationary response dynamics.

THE ROLE OF THE NUCLEAR MATTER COMPRESSION MODULUS IN NEUTRON STARS

2004 ◽  
Vol 13 (07) ◽  
pp. 1519-1524 ◽  
Author(s):  
VERÔNICA A. DEXHEIMER ◽  
CÉSAR A. Z. VASCONCELLOS ◽  
MOISÉS RAZEIRA ◽  
MANFRED DILLIG
Keyword(s):  
Neutron Stars ◽  
Nuclear Matter ◽  
Body Problem ◽  
Mean Field Theory ◽  
Mean Field ◽  
Compression Modulus ◽  
Baryon Number ◽  
Many Body ◽  
Relativistic Mean Field

For the nuclear many body problem at high densities, formulated in the framework of a relativistic mean-field theory, we investigate in detail the compression modulus of nuclear matter as a function of the effective nucleon mass. We include consistently in our modelling chemical equilibrium as well as baryon number and electric charge conservation and investigate properties of neutron stars. Among other predictions we focus on the dependence of the maximum mass of a sequence of neutron stars as a function of the compression modulus and the nucleon effective mass.

scholarly journals Quantum Many-Body Theory for Exciton-Polaritons in Semiconductor Mie Resonators in the Non-Equilibrium

2020 ◽  
Vol 10 (5) ◽  
pp. 1836 ◽  
Author(s):  
Andreas Lubatsch ◽  
Regine Frank
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Many Body ◽  
Thermodynamical Equilibrium ◽  
Electronic Density ◽  
Many Body Theory ◽  
Exciton Polaritons ◽  
Gain Narrowing ◽  
Lasing Modes ◽  
Non Equilibrium

We implement externally excited ZnO Mie resonators in a framework of a generalized Hubbard Hamiltonian to investigate the lifetimes of excitons and exciton-polaritons out of thermodynamical equilibrium. Our results are derived by a Floquet-Keldysh-Green’s formalism with Dynamical Mean Field Theory (DMFT) and a second order iterative perturbation theory solver (IPT). We find that the Fano resonance which originates from coupling of the continuum of electronic density of states to the semiconductor Mie resonator yields polaritons with lifetimes between 0.6 ps and 1.45 ps. These results are compared to ZnO polariton lasers and to ZnO random lasers. We interpret the peaks of the exciton-polariton lifetimes in our results as a sign of gain narrowing which may lead to stable polariton lasing modes in the single excited ZnO Mie resonator. This form of gain may lead to polariton random lasing in an ensemble of ZnO Mie resonators in the non-equilibrium.

scholarly journals Hydrophobic droplets in amphiphilic bilayers: a coarse-grained mean-field theory study

Soft Matter ◽  
2012 ◽  
Vol 8 (12) ◽  
pp. 3308 ◽  
Author(s):  
Martin J. Greenall ◽  
Carlos M. Marques
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Coarse Grained

Mesoscale Simulation of Morphology in Hydrated Perfluorosulfonic Acid Membranes

2005 ◽  
Vol 885 ◽  
Author(s):  
James T. Wescott ◽  
Yue Qi ◽  
Lalitha Subramanian ◽  
T. Weston Capehart
Keyword(s):  
Mesoscale Model ◽  
Random Network ◽  
Mean Field Theory ◽  
Mean Field ◽  
Domain Size ◽  
Proton Exchange ◽  
Coarse Grained ◽  
Perfluorosulfonic Acid ◽  
Perfluorosulfonic Acid Membranes ◽  
Hydrophilic Domain

ABSTRACTCurrent fuel cell proton exchange membranes (PEM) rely on a random network of conducting hydrophilic domains to transport protons across the membrane. Despite extensive investigation, details of the structure of the hydrophilic domains in these membranes remain unresolved. In this study a dynamic self-consistent mean field theory has been applied to obtain the morphologies of hydrated Perfluorosulfonic Acid (PFSA) (equivalent weight of 1100) as a model for Nafion® at several water contents. A coarse-grained mesoscale model was developed by dividing the system into three components: backbone, side chain, and water. The interaction parameters for this model were generated using classical molecular dynamics. The simulated morphology shows phase separated micelles filled with water, surrounded by side chains containing sulfonic groups, and embedded in the fluorocarbon matrix. For λ<6 (λ gives the ratio of water molecules to sulfonic groups), the isolated domains obtained from simulation are nearly spherical with a domain size smaller than that fitted to experimental SANS data. For λ>8; the domains deform into elliptical and barbell shapes as they merge. The simulated morphology, hydrophilic domain size and shape are generally consistent with some experimental observations.

Calculation of the propagation amplitude in the case of a Coulomb interaction via time-independent mean-field theory

2007 ◽  
Vol 85 (7) ◽  
pp. 787-796
Author(s):  
R Yekken ◽  
F Mekideche
Keyword(s):  
Coulomb Interaction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Numerical Comparison ◽  
Many Body ◽  
Field Equations ◽  
Range Interaction ◽  
Approximate Methods ◽  
Mean Field Equations ◽  
Many Body Systems

The exact study of many-body microscopic systems is impossible when the number of particles is large (N ≥ 3). Approximate methods are then used. The time-independent mean-field (TIMF) approximation has been proposed for the description of collisions in many-body systems. Collision amplitudes are derived by the use of a variational principle and the choice of trial functions as products of single-particle orbitals. Resulting mean-field equations with a nonvanishing right-hand side turn out to be a generalization of the traditional Hartree or Hatree–Fock type equations. These TIMF equations are successfully solved numerically for the case of short-range forces. In this paper, we test the validity of this theory for the Coulomb interaction between two particles, that is, a long-range interaction. A numerical comparison between the exact and the mean-field solutions is conducted PACS Nos.: 31.15.Ne, 31.15.Pf, 21.45.+v,25.10.-i

scholarly journals NEW RANDOM ORDERED PHASE IN ISOTROPIC MODELS WITH MANY-BODY INTERACTIONS

2011 ◽  
Vol 25 (01) ◽  
pp. 73-82 ◽  
Author(s):  
YOICHIRO HASHIZUME ◽  
MASUO SUZUKI
Keyword(s):  
Random Systems ◽  
Mean Field Theory ◽  
Mean Field ◽  
New Order ◽  
Many Body ◽  
Spin Correlations ◽  
Spin Pair ◽  
The Mean ◽  
Many Body Interactions ◽  
Physical Quantities

In this study, we have found a new random ordered phase in isotropic models with many-body interactions. Spin correlations between neighboring planes are rigorously shown to form a long-range order, namely coplanar spin-pair order, using a unitary transformation, and the phase transition of this new order has been analyzed on the bases of the mean-field theory and correlation identities. In the systems with regular 4-body interactions, the transition temperature T c is obtained as T c = (z-2)J/k B , and the field conjugate to this new order parameter is found to be H2. In contrast, the corresponding physical quantities in the systems with random 4-body interactions are given by [Formula: see text] and H4, respectively. Scaling forms of order parameters for regular or random 4-body interactions are expressed by the same scaling functions in the systems with regular or random 2-body interactions, respectively. Furthermore, we have obtained the nonlinear susceptibilities in the regular and random systems, where the coefficient χnl of H3 in the magnetization shows positive divergence in the regular model, while the coefficient χ7 of H7 in the magnetization shows negative divergence in the random model.

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