Igor V. Ovchinnikov

A Liouville equation for systems which exchange particles with reservoirs: Transport through a nanodevice

A Redfield-like Liouville equation for an open system that couples to one or more leads and exchanges particles with them is derived. The equation is presented for a general case. A case study of time-dependent transport through a single quantum level for varying electrostatic and chemical potentials in the leads is presented. For the case of varying electrostatic potentials the proposed equation yields, for the model study, the results of an exact solution.

Variability of electronics and spintronics nanoscale devices

We address the problem of how the quantum (and the temperature) fluctuations will affect the magnetoelectronic circuits’ operation, and if there are any advantages, or possibly drawbacks, in the switching from the charge for uncorrelated electronics to the spin for spintronics. Within the framework of “minimal” ferromagnetic Hamiltonian, we consider the fluctuations in the total number of the electrons on the gate, the total spin, and the spin vector projection on the easy axis. It is expected that spintronics devices will improve variability compared with today’s electronics devices.

Introduction to Supersymmetric Theory of Stochastics

Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This orders omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence,

Spintronics birefringence with an extended molecular loop-wire or spiral coupling

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Voltage-controlled surface magnetization of itinerant ferromagnet Ni1-xCux

noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized criticality, etc. Although several successful approaches to various realizations of DLRO have been established, the universal theoretical understanding of this phenomenon remained elusive. The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS). There, DLRO is the spontaneous breakdown of the topological or de Rham supersymmetry that all stochastic differential equations (SDEs) possess. This theory may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity. The STS is also an interdisciplinary construction. This theory is based on dynamical systems theory, cohomological field theories, the theory of pseudo-Hermitian operators, and the conventional theory of SDEs. Reviewing the literature on all these mathematical disciplines can be time-consuming. As such, a concise and self-contained introduction to the STS, the goal of this paper, may be useful.

Topological Field Theory and Computing with Instantons

A ring with spin-orbit effects coupled to a conducting wire is shown to exhibit a phase delay which is spin dependent. The key is that the coupling of the ring to the wire is over an extended spatial range and not just along a single point; this breaks the symmetry and makes the ring states couple differently to forward and backward moving wire states. This results, for properly injected spin states, in a spin-flipping probability which is dependent on the energy of the injected electron and can therefore be easily controlled. Several systems are presented and shown to exhibit this effect including the basic ring which couples to a wire as well as a ring which mediates between two wires, and a spiral between two wires.

Voltage-controlled ferromagnetic order in MnGe quantum dots.

We argue that surface magnetization of a metallic ferromagnet can be turned on and off isothermally by an applied voltage. For this, the materials electron subsystem must be close enough to the boundary between para- and ferromagnetic regions on the electron density scale. For the 3d series, the boundary is between Ni and Cu, which makes their alloy a primary candidate. Using Ginzburg-Landau functional, which we build from Ni_(1-x)Cu_x empirical properties, ab-initio parameters of Ni and Cu, and orbital-free LSDA, we show that the proposed effect is experimentally observable.

Hydrodynamic tensor density functional theory with correct susceptibility

Chern-Simons topological field theories TFTs are the only TFTs that have already found application in the description of some exotic strongly-correlated electron systems and the corresponding concept of topological quantum computing. Here, we show that TFTs of another type, specifically the gauge-field-less Witten-type TFTs known as topological sigma models, describe the recently proposed digital memcomputing machines (DMMs) - engineered dynamical systems with point attractors being the solutions of the corresponding logic circuit that solves a specific task. This result derives from the recent finding that any stochastic differential equation possesses a topological supersymmetry, and the realization that the solution search by a DMM proceeds via an instantonic phase. Certain TFT correlators in DMMs then reveal the presence of a transient long-range order both in space and time, associated with the effective breakdown of the topological supersymmetry by instantons. The ensuing non-locality and the low dimensionality of instantons are the physical reasons why DMMs can solve complex problems efficiently, despite their non-quantum character. We exemplify these results with the solution of prime factorization.

Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics

Here, we speculate that room temperature voltage-controlled ferromagnetic ordering may become a founding phenomenon for the next generation of low-power spintronics nanodevices and discuss the special role of dilute magnetic semiconductors as the most reliable material basis to date. Then, we report on our latest experimental achievements in the voltage manipulation of the ferromagnetism in MnGe quantum dots, experimentally demonstrating the capacity of pushing the Curie temperature further above room temperature for technological applications.

Comparison of spintronics and nanoelectronics for information processing

In a previous work the authors developed a family of orbital-free tensor equations for the density functional theory [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equation hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work the authors assumed that the cumulants vanish above a certain order (N). Here the authors show how to modify this assumption to obtain the correct susceptibilities. This is done for N=3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a nonperturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained, while the Thomas-Fermi and von Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N=3 level demonstrate the authors previous assertion that as the order of the theory is increased new additional transverse sound modes appear mimicking the random phase approximation transverse dispersion region.