scholarly journals Polaron Models with Regular Interactions at Strong Coupling

2021 ◽  
Vol 186 (1) ◽  
Author(s):  
Krzysztof Myśliwy ◽  
Robert Seiringer
Keyword(s):  
Effective Mass ◽  
Strong Coupling ◽  
State Energy ◽  
Asymptotic Form ◽  
Phonon Dispersion ◽  
Semiclassical Approximation ◽  
Strong Coupling Limit ◽  
Leading Order ◽  
Regular Form ◽  
Spatial Dimensions

AbstractWe study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.

scholarly journals On the strong coupling limit of many-polaron systems in electromagnetic fields

2015 ◽  
Vol 27 (02) ◽  
pp. 1550005 ◽  
Author(s):  
D. Wellig
Keyword(s):  
Strong Coupling ◽  
Electromagnetic Fields ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Strong Coupling Limit ◽  
Coupling Constants ◽  
Minimal Energy ◽  
Strong Magnetic Fields ◽  
Large Coupling

In this paper, estimates on the ground state energy of Fröhlich N-polarons in electromagnetic fields in the strong coupling limit, α → ∞, are derived. It is shown that the ground state energy is given by α2 multiplied by the minimal energy of the corresponding Pekar–Tomasevich functional for N particles, up to an error term of order α42/23 N3. The potentials A, V are suitably rescaled in α. As a corollary, binding of N-polarons for strong magnetic fields for large coupling constants is established.

MULTI-DIMENSIONAL FRÖHLICH BIPOLARON AND DIMENSIONAL SCALING

1990 ◽  
Vol 04 (11n12) ◽  
pp. 1879-1888 ◽  
Author(s):  
SHREEKANTHA SIL ◽  
ASHOK CHATTERJEE
Keyword(s):  
Effective Mass ◽  
Strong Coupling ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Three Dimensions ◽  
Scaling Relations ◽  
Dimensional Scaling ◽  
Polar Crystal ◽  
Fröhlich Bipolaron

The formation and stability of the Fröhlich bipolaron in a multi-dimensional polar crystal is investigated within the framework of strong coupling Landau-Pekar theory. The ground state energy, the effective mass and the size of the bipolaron are calculated. It is shown that Fröhlich bipolarons can exist in both two and three dimensions, the bipolaronic binding being stronger in lower dimensions. The dimensional scaling relations satisfied by the ground state energy and the effective mass of the bipolaron are also obtained.

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

TOPOLOGY OF THE GRASSMANNIAN σ MODEL ON A LATTICE

1987 ◽  
Vol 02 (08) ◽  
pp. 601-608 ◽  
Author(s):  
T. FUKAI ◽  
M. V. ATRE
Keyword(s):  
Partition Function ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Limit ◽  
Topological Term

The Grassmannian σ model with a topological term is studied on a lattice. The θ dependence of the partition function and the Wilson loop are evaluated in the strong coupling limit. The latter is shown to be independent of the area at θ = π, as in the CPN−1 model.

scholarly journals Fundamental limitations of the mode temperature concept in strongly coupled systems

2020 ◽  
Vol 75 (8) ◽  
pp. 803-807
Author(s):  
Svend-Age Biehs ◽  
Achim Kittel ◽  
Philippe Ben-Abdallah
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Strong Coupling ◽  
Quantum Systems ◽  
Coupled Systems ◽  
Strong Coupling Limit ◽  
Strongly Coupled ◽  
Fundamental Limitations ◽  
Temperature Concept ◽  
Vacuum Gap

AbstractWe theoretically analyze heat exchange between two quantum systems in interaction with external thermostats. We show that in the strong coupling limit the widely used concept of mode temperatures loses its thermodynamic foundation and therefore cannot be employed to make a valid statement on cooling and heating in such systems; instead, the incorrectly applied concept may result in a severe misinterpretation of the underlying physics. We illustrate these general conclusions by discussing recent experimental results reported on the nanoscale heat transfer through quantum fluctuations between two nanomechanical membranes separated by a vacuum gap.

Sign in / Sign up

Export Citation Format

Share Document