Crossover from non-Fermi liquid to Fermi liquid behavior close to a quantum critical point: A brief review

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a nesting vector Q and the interaction between electrons gives rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a quantum critical point is obtained as the Néel temperature tends to zero. We review our results on the specific heat, the quasi-particle linewidth, the electrical resistivity, the amplitudes of de Haas-van Alphen oscillations and the dynamical spin susceptibility.     

Crossover from adiabatic to sudden interaction quench in a Luttinger liquid

Motivated by recent experiments on interacting cold atoms, we analyze interaction quenches in Luttinger liquids (LLs), where the interaction is ramped from zero to a finite value within a finite time. The fermionic single particle density matrix reveals several regions of spatial and temporal coordinates relative to the quench time, termed as Fermi liquid, sudden quench LL, adiabatic LL regime, and a LL regime with a time-dependent exponent. The various regimes can also be observed in the momentum distribution of the fermions, directly accessible through time of flight experiments. Most of our results apply to arbitrary quench protocols.     

Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

Crossover from quantum to classical transport

Understanding the crossover from quantum to classical transport has become of fundamental importance not only for technological applications due to the creation of sub-10-nm transistors – an important building block of our modern life – but also for elucidating the role played by quantum mechanics in the evolutionary fitness of biological complexes. This article provides a basic introduction into the nature of charge and energy transport in the quantum and classical regimes. It discusses the characteristic transport properties in both limits and demonstrates how they can be connected through the loss of quantum mechanical coherence. The salient features of the crossover physics are identified, and their importance in opening new transport regimes and in understanding efficient and robust energy transport in biological complexes are demonstrated.     

Speculations of crossover from mean-field to critical behavior for long-range site percolation

We argue that for percolation, in contrast to thermal phase transitions, long-range forces do not lead to classical (Bethe lattice) exponents at the phase transition.     

Modeling ternary mixtures by mean-field theory of polyelectrolytes: Coupled Ginzburg-Landau and Swift-Hohenberg equations

The purpose of this work is to model ternary mixtures using the theory of pattern formation and of polyelectrolytes, with mean-field approximations. The model has two local, non-conserved order parameters. In the free energy short-range and long-range nonlocal interactions between elements of the mixture are considered. The spatiotemporal dynamics of the system is described by coupling the time-dependent Ginzburg-Landau equation and the Swift-Hohenberg equation. These non-linear partial differential equations are solved with numerical methods to study the emergent spatially stable configurations. The model shows a large diversity of patterns, which permit an interpretation of the behavior of some biological systems and presents different growth lengths within its spatial structures.     

Crossover from intermittent to continuum dynamics for locally driven colloids

We simulate a colloid with charge q(d) driven through a disordered assembly of interacting colloids with charge q and show that, for q(d) approximately q, the velocity-force relation is nonlinear and the velocity fluctuations of the driven particle are highly intermittent with a 1/f characteristic. When g(d) >q , the average velocity drops, the velocity-force relation becomes linear, and the velocity fluctuations are Gaussian. We discuss the results in terms of a crossover from strongly intermittent heterogeneous dynamics to continuum dynamics. We also make several predictions for the transient response in the different regimes.     

On the critical exponents for the λ transition in liquid helium

The use of a new method for summing divergent series makes it possible to significantly increase the accuracy of determining the critical exponents from the field theoretical renormalization group. The exponent value ν = 0.6700 ± 0.0006 for the λ transition in liquid helium is in good agreement with the experiment, but contradicts the last theoretical results based on using high-temperature series, the Monte Carlo method, and their synthesis.     

Crossover from BCS superconductivity to Bose-Einstein condensation: A self-consistent theory

A dilute three-dimensional Fermi liquid is considered with an instantaneous attractive short-range interaction. Two sets of self-consistent equations for the temperature dependent fermion Greens functiong and the four-point vertex function are derived by field theoretic means. The interaction is taken into account using the results of low energys-wave scattering theory. The crossover region between BCS superconductivity and Bose-Einstein condensation of tightly bound pairs is located near the threshold where in the two-particle scattering problem a virtual or quasi-stationary state turns into a bound state. We show how from our self-consistent equations the BCS theory and the theory of a superfluid Bose gas can be recovered in the weak and strong coupling limit, respectively. In the strong coupling limit we find that there is a repulsive interaction between the composite bosons due to the Pauli exclusion principle. It is described by a positive scattering lengtha _B which is twice the scattering length of the fermions,a _B =2a _F . Furthermore we find that this interaction reduces the Bose-Einstein transition temperature to leading order by T _c /T _{c, BE} =–(k _F a _F )³/3. We show that most of the previous theories of the crossover scenario can be obtained from our theory in mean-field approximation neglecting self consistency.     

Crossover from Mott to Efros-Shklovskii variable range-hopping in Si:P

The low-temperature conductivity of uncompensated insulating Si:P with P concentration just below the metal-insulator (MI) transition shows with decreasingN a crossover from Mott variable range hopping (VRH) to Efros-Shklovskii VRH. From the concentration dependence of the Mott temperatureT _M a correlation-length exponent ν=1.1 is obtained which is compatible with the conductivity exponent μ=1.3 for metallic samples.     

NpT-ensemble Monte Carlo calculations for binary liquid mixtures

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12-6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.     

Universality of 3D percolation exponents and first-order corrections to scaling for conductivity exponents

By using a fast, Nested Dissection algorithm we compare the results of finite-size scaling at p_c and of “p” scaling () on large cubic random resistor networks [up to 500×500×500]. The “p” scaling for conductivity of both site and bond networks leads to an exponent t=2.00(1). The finite-size scaling leads to the ratio of this conductivity exponent to the coherence length exponent ν: t/ν=2.283(3). Combining these results we estimate ν=0.876(6), in excellent agreement with a value proposed by Ballesteros et al. The first-order correctional exponent ω is found to be ω=1.0(2).     

Crossover from one to three dimensions for a gas of hard-core bosons

We develop a variational theory of the crossover from the one-dimensional (1D) regime to the 3D regime for ultracold Bose gases in thin waveguides. Within the 1D regime we map out the parameter space for fermionization, which may span the full 1D regime for suitable transverse confinement.