Elena V. Kirichenko

High-magnetic-fields thermodynamics of the heavy-fermion metal YbRh2Si2

We perform a comprehensive theoretical analysis of the high-magnetic-field behavior of the heavy-fermion (HF) compound YbRh2Si2. At low magnetic fields B, YbRh2Si2 has a quantum critical point related to the suppression of antiferromagnetic ordering at a critical magnetic field B⊥c of B=Bc00.06 T. Our calculations of the thermodynamic properties of YbRh2Si2 in wide magnetic field range from Bc00.06 T to B18 T allow us to straddle a possible metamagnetic transition region and probe the properties of both low-field HF liquid and high-field fully polarized one. Namely, high magnetic fields B~B*~10 T fully polarize the corresponding quasiparticle band generating a Landau-Fermi-liquid (LFL) state and suppressing the HF (actually NFL) one, while at increasing temperatures both the HF state and the corresponding NFL properties are restored. Our calculations are in good agreement with experimental facts and show that the fermion condensation quantum phase transition is indeed responsible for the observed NFL behavior and quasiparticles survive both high temperatures and high magnetic fields.

Lévy flights in an infinite potential well as a hypersingular Fredholm problem.

We study Lévy flights with arbitrary index 0<μ≤2 inside a potential well of infinite depth. Such a problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schrödinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain D, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numerically with some analytical results regarding the structure of the spectrum.

Quasi-one-dimensional quantum spin liquid in the Cu(C4H4N2)(NO3)2 insulator

We analyze measurements of the magnetization, differential susceptibility and specific heat of quasi-onedimensional insulator Cu(C4H4N2)(NO3)2 (CuPzN) subjected to magnetic fields. We show that the thermodynamic properties are defined by quantum spin liquid formed with spinons, with the magnetic field tuning the insulator CuPzN towards quantum critical point related to fermion condensation quantum phase transition (FCQPT) at which the spinon effective mass diverges kinematically. We show that the FCQPT concept permits to reveal and explain the scaling behavior of thermodynamic characteristics. For the first time, we construct the schematic T–H (temperature-magnetic field) phase diagram of CuPzN that contains Landau–Fermi-liquid, crossover and non-Fermi liquid parts, thus resembling that of heavy-fermion compounds.

Ultrarelativistic (Cauchy) Spectral Problem in the Infinite Well

We analyze spectral properties of the ultrarelativistic (Cauchy) operator

Physical properties of ferroelectric film with continuous space charge distribution

|\Delta |^{1/2}

The influence of quantum fluctuations on phase transition temperature in disordered ferroelectrics

, provided its action is constrained exclusively to the interior of the interval

Photoinduced magnetization wave in diluted magnetic semiconductors

[-1,1] \subset R

Magnetic quantum criticality in quasi‐one‐dimensional Heisenberg antiferromagnet Cu (C4H4N2)( NO 3)2

. To this end both analytic and numerical methods are employed. New high-accuracy spectral data are obtained. A direct analytic proof is given that trigonometric functions

Quantum critical point in CePd1-xRhx ferromagnet

\cos(n\pi x/2)

Infinite Cauchy well spectral solution as the hypersingular Fredholm problem

and