Singlet-triplet conversion and the long-range proximity effect in superconductor-ferromagnet structures with generic spin dependent fields.

The long-range proximity effect in superconductor-ferromagnet (S/F) hybrid nanostructures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the ferromagnet over large distances. It is commonly believed that this happens only in the presence of magnetic inhomogeneities. We show that there are other sources of the long-range triplet component (LRTC) of the condensate and establish general conditions for their occurrence. As a prototypical example, we consider first a system where the exchange field and spin-orbit coupling can be treated as time and space components of an effective SU(2) potential. We derive a SU(2) covariant diffusive equation for the condensate and demonstrate that an effective SU(2) electric field is responsible for the long-range proximity effect. Finally, we extend our analysis to a generic ferromagnet and establish a universal condition for the LRTC. Our results open a new avenue in the search for such correlations in S/F structures and make a hitherto unknown connection between the LRTC and Yang-Mills electrostatics.

Time-dependent density functional theory for many-electron systems interacting with cavity photons.

Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows us to calculate the above basic variables by solving self-consistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems. In particular we show that it naturally leads to time-dependent density functional theory for systems coupled to the Caldeira-Leggett bath.

Quantum continuum mechanics made simple.

In this paper we further explore and develop the quantum continuum mechanics (QCM) of Tao et al. [Phys. Rev. Lett. 103, 086401 (2009)] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the QCM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham (KS) version. We use the simplified approach to directly prove the exactness of QCM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the QCM theory and their implication on QCM-based approximations. The one-electron proof then motivates an approximation to the QCM (exact under certain conditions) expanded on the wavefunctions of the KS equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the QCM. We also demonstrate the simplified QCM semianalytically on an example system.

Exact Kohn-Sham potential of strongly correlated finite systems.

The dissociation of molecules, even the most simple hydrogen molecule, cannot be described accurately within density functional theory because none of the currently available functionals accounts for strong on-site correlation. This problem led to a discussion of properties that the local Kohn-Sham potential has to satisfy in order to correctly describe strongly correlated systems. We derive an analytic expression for the nontrivial form of the Kohn-Sham potential in between the two fragments for the dissociation of a single bond. We show that the numerical calculations for a one-dimensional two-electron model system indeed approach and reach this limit. It is shown that the functional form of the potential is universal, i.e., independent of the details of the two fragments.

Linear continuum mechanics for quantum many-body systems.

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally comoving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.

Time-dependent current density functional theory via time-dependent deformation functional theory: a constrained search formulation in the time domain.

The logical structure and basic theorems of time-dependent current density functional theory (TDCDFT) are analyzed and reconsidered from the point of view of recently proposed time-dependent deformation functional theory (TDDefFT). It is shown that the formalism of TDDefFT allows to avoid a traditional external potential-to-density/current mapping. Instead the theory is formulated in a form similar to the constrained search procedure in the ground state DFT. Within this formulation of TDCDFT all basic functionals appear from the solution of a constrained universal many-body problem in a comoving reference frame, which is equivalent to finding a conditional extremum of a certain universal action functional. As a result the physical origin of the universal functionals entering the theory, as well as their proper causal structure become obvious. In particular, this leaves no room for any doubt concerning the predictive power of the theory.

Lorentz shear modulus of fractional quantum Hall states.

We show that the Lorentz shear modulus of macroscopically homogeneous electronic states in the lowest Landau level is proportional to the bulk modulus of an equivalent system of interacting classical particles in the thermodynamic limit. Making use of this correspondence, we calculate the Lorentz shear modulus of Laughlin's fractional quantum Hall states at filling factor ν = 1/m (m an odd integer) and find that it is equal to [Formula: see text], where n is the density of particles and the sign depends on the direction of magnetic field.

Equilibrium spin currents: non-Abelian gauge invariance and color diamagnetism in condensed matter.

The spin-orbit (SO) interaction acts on electrons in condensed matter as an effective non-Abelian field. I show that a magnetic component of this field inevitably generates diamagnetic color currents which are just the equilibrium spin currents discussed in a condensed matter context. Since the non-Abelian magnetic field generated by SO coupling is generically nonzero, the equilibrium spin currents are universally present in any physical system, e.g., in molecules or solids with SO interaction. These universal spin currents provide an explicit realization of a non-Abelian Landau diamagnetism.

Quantum stress focusing in descriptive chemistry.

We show that several important concepts of descriptive chemistry, such as atomic shells, bonding electron pairs, and lone electron pairs, may be described in terms of quantum stress focusing, i.e., the spontaneous formation of high-pressure regions in an electron gas. This description subsumes previous mathematical constructions, such as the Laplacian of the density and the electron localization function, and provides a new tool for visualizing chemical structure. We also show that the full stress tensor, defined as the derivative of the energy with respect to a local deformation, can be easily calculated from density functional theory.

New collective mode in the fractional quantum Hall liquid.

We apply the methods of continuum mechanics to the study of the collective modes of the fractional quantum Hall liquid. Our main result is that at long-wavelength, there are two distinct modes of oscillations, while previous theories predicted only one. The two modes are shown to arise from the internal dynamics of shear stresses created by the Coulomb interaction in the liquid. Our prediction is supported by recent light scattering experiments, which report the observation of two long-wavelength modes in a quantum Hall liquid.

Dilute Fermi gas in quasi-one-dimensional traps: from weakly interacting fermions via hard core bosons to a weakly interacting Bose gas.

We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size l(perpendicular). In the dilute limit (nl(perpendicular)<<1, where n is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length aF. When l(perpendicular)/aF goes from -infinity to +infinity, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at aF approximately +/-nl2(perpendicular). In conclusion, we discuss experimental implications of these results.

Many-body diagrammatic expansion in a kohn-sham basis: implications for time-dependent density functional theory of excited states.

We formulate diagrammatic rules for many-body perturbation theory which uses Kohn-Sham Green's functions as basic propagators. The diagram technique allows one to study the properties of the dynamic nonlocal exchange-correlation (xc) kernel f(xc). We show that the spatial nonlocality of f(xc) is strongly frequency dependent. In particular, in extended systems the nonlocality range diverges at the excitation energies. This divergency is related to the discontinuity of the xc potential.