Vladimir Privman

Finite size scaling and numerical simulation of statistical systems

The theory of Finite Size Scaling describes a build-up of the bulk properties when a small system is increased in size. This description is particularly important in strongly correlated systems where critical fluctuations develop with increasing system size, including phase transition points, polymer conformations. Since numerical computer simulations are always done with finite samples, they rely on the Finite Size Scaling theory for data extrapolation and analysis. With the advent of large scale computing in recent years, the use of the size-scaling methods has become increasingly important.

Nonequilibrium statistical mechanics in one dimension

Part I. Reaction-Diffusion Systems and Models of Catalysis 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham 3. Critical phenomena at absorbing states R. Dickman Part II. Kinetic Ising Models 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz 5. Glauber dynamics of the ising model N. Ito 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell Part III. Ordering, Coagulation, Phase Separation 7. Phase-ordering dynamics in one dimension A. J. Bray 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu Part IV. Random Sequential Adsorption and Relaxation Processes 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans 11. Lattice models of irreversible adsorption and diffusion P. Nielaba 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma Part V. Fluctuations In Particle and Surface Systems 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans 15. Nonequilibrium surface dynamics with volume conservation J. Krug 16. Directed walks models of polymers and wetting J. Yeomans Part VI. Diffusion and Transport In One Dimension 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston 19. One-dimensional random walks in random environment K. Ziegler Part VII. Experimental Results 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman Index.

Finite-size effects at first-order transitions

Finite-size rounding of a first-order phase transition is studied in “block”- and “cylinder”-shaped ferromagnetic scalar spin systems. Crossover in shape is investigated and the universal form of the rounded susceptibility peak is obtained. Scaling forms on the low-temperature side of the critical point are considered both above and below the borderline dimensionality,d>=4. A method of phenomenological renormalization, applicable to both odd and even field derivatives, is suggested and used to estimate universal amplitudes for two-dimensional Ising models atT=Tc.

QUANTUM COMPUTATION IN QUANTUM-HALL SYSTEMS

Abstract We describe a quantum information processor (quantum computer) based on the hyperfine interactions between the conduction electrons and nuclear spins embedded in a two-dimensional electron system in the quantum-Hall regime. Nuclear spins can be controlled individually by electromagnetic pulses. Their interactions, which are of the spin-exchange type, can be possibly switched on and off pair-wise dynamically, for nearest neighbors, by controlling impurities. We also propose the way to feed in the initial data and explore ideas for reading off the final results.

Random sequential adsorption: from continuum to lattice and pre-patterned substrates

The random sequential adsorption (RSA) model has served as a paradigm for diverse phenomena in physical chemistry, as well as in other areas such as biology, ecology, and sociology. In the present work, we survey aspects of the RSA model with emphasis on the approach to and properties of jammed states obtained for large times in continuum deposition versus that on lattice substrates, and on pre-patterned surfaces. The latter model has been of recent interest in the context of efforts to use pre-patterning as a tool to improve self-assembly in micro- and nanoscale surface structure engineering.

Effect of spin-orbit interaction and in-plane magnetic field on the conductance of a quasi-one-dimensional system

We study the effect of spin-orbit interaction and in-plane effective magnetic field on the conductance of a quasi-one-dimensional ballistic electron system. The effective magnetic field includes the externally applied field, as well as the field due to polarized nuclear spins. The interplay of the spin-orbit interaction with effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps, introducing the dependence of the subband energies on the field direction. We generalize the Landauer formula at finite temperatures to incorporate these special features of the dispersion relation. The obtained formula describes the conductance of a ballistic conductor with an arbitrary dispersion relation.

Particle adhesion in model systems. Part 13.—Theory of multilayer deposition

A model is developed to describe multilayer deposition in packed-bed systems. The multilayer deposition is significant for colloid suspensions which are near or beyond the critical coagulation conditions. Packed-bed deposition studies of such suspensions are possible in experiments with short residence times. Our model is formulated along the lines of the existing monolayer theories and involves one new parameter which characterizes the multilayer adhesion probability.

Enzymatic AND Logic Gates Operated Under Conditions Characteristic of Biomedical Applications

Experimental and theoretical analyses of the lactate dehydrogenase and glutathione reductase based enzymatic AND logic gates in which the enzymes and their substrates serve as logic inputs are performed. These two systems are examples of the novel, previously unexplored class of biochemical logic gates that illustrate potential biomedical applications of biochemical logic. They are characterized by input concentrations at logic 0 and 1 states corresponding to normal and pathophysiological conditions. Our analysis shows that the logic gates under investigation have similar noise characteristics. Both significantly amplify random noise present in inputs; however, we establish that for realistic widths of the input noise distributions, it is still possible to differentiate between the logic 0 and 1 states of the output. This indicates that reliable detection of pathophysiological conditions is indeed possible with such enzyme logic systems.

Indirect Interaction of Solid-State Qubits via Two-Dimensional Electron Gas

We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.

Semiclassical Monte Carlo model for in-plane transport of spin-polarized electrons in III–V heterostructures

We study the in-plane transport of spin-polarized electrons in III–V semiconductor quantum wells. The spin dynamics is controlled by the spin-orbit interaction, which arises due to the bulk crystalline-structure asymmetry and quantum-well inversion asymmetry. This interaction, owing to its momentum dependence, causes rotation of the spin-polarization vector, and also produces effective spin dephasing. The density matrix approach is used to describe the evolution of the electron spin polarization, while the spatial motion of the electrons is treated semiclassically. Monte Carlo simulations have been carried out for temperatures in the range 77–300 K.