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Vladimir Privman

Publications and source records attributed to Vladimir Privman.

At least 109 records · Page 6Linked to original sources
arXiv2002

Relaxation of Shallow Donor Electron Spin due to Interaction with Nuclear Spin Bath

We study the low-temperature dynamics of a shallow donor, e.g., $^{31}$P, impurity electron spin in silicon, interacting with the bath of nuclear spins of the $^{29}$Si isotope. For small applied magnetic fields, the electron spin relaxation is controlled by the steady state distribution of the nuclear spins. We calculate the relaxation times $T_1$ and $T_2$ as functions of the external magnetic field, and conclude that nuclear spins play an important role in the donor electron spin decoherence in Si:P at low magnetic fields.

cond-mat.mes-hall↗
arXiv2001

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

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

cond-mat.mes-hall↗
arXiv2001

Model of Formation of Monodispersed Colloids

Ample experimental evidence has been accumulated demonstrating that the formation of monodispersed colloids proceeds through a more complex mechanism, than the generally excepted diffusional "burst nucleation" process. Instead, the synthesis of narrow-size-distribution colloidal dispersions involves several stages, i.e., nuclei produced in a supersaturated solution, grow to nanosize subunits, which then aggregate to form much larger uniform secondary particles. To explain the size selection in such a series of processes, a kinetic model was developed which combined two growth/aggregation stages. This earlier study has shown the burst-nucleation growth of the primary particles to depend strongly on the value of the effective surface tension entering the surface term in the free energy of the subcritical embryos. The aim of the present work has been to identify an appropriate control parameter in the process of secondary particle aggregation. Modifications of the aggregation rates to account for singlet size and aggregate diffusivity produced only small changes. However, introduction of a "bottle-neck" factor in the dimer formation rate had a profound effect on the final size distribution and suggested a possible size-control mechanism.

cond-mat.mtrl-sci↗
arXiv2001

Semiconductor quantum computer design with 100 nm separation of nuclear-spin qubits

We combine elements of the 1998 quantum computing proposals by Privman, Vagner and Kventsel, and by Kane, with the new idea of nuclear-spin qubit interactions mediated indirectly via the bound outer electrons of impurity atoms whose nuclear spins 1/2 are the qubits. These electrons, in turn, interact via the two-dimensional electron gas in the quantum Hall effect regime. The resulting quantum computing scheme retains all the gate-control and measurement aspects of the proposal by Kane, but allows qubit spacing at distances of order 100 nm, attainable with the present-day semiconductor-heterostructure device technologies.

quant-ph↗
arXiv2001

Quantum computing with spin qubits in semiconductor structures

We survey recent work on designing and evaluating quantum computing implementations based on nuclear or bound-electron spins in semiconductor heterostructures at low temperatures and in high magnetic fields. General overview is followed by a summary of results of our theoretical calculations of decoherence time scales and spin-spin interactions. The latter were carried out for systems for which the two-dimensional electron gas provides the dominant carrier for spin dynamics via exchange of spin-excitons in the integer quantum Hall regime.

cond-mat.mes-hall↗
arXiv2001

Boundary Conditions in Diffusional Growth and Sedimentation

In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or sediments, particles in the suspension outside the surface or aggregate boundary can be considered as diffusing under the influence of applied forces, such as the double-layer interactions or gravity. However, the diffusion equation cannot be used at the substrate or inside the aggregate. One convenient and widely used approach has been to impose boundary conditions at the surface, to supplement and completely define the diffusion problem outside it. This short survey describes some theoretical results on the use of such boundary conditions and their physical interpretation.

cond-mat↗
arXiv2000

Decoherence and Measurement in Open Quantum Systems

We review results of a recently developed model of a microscopic quantum system interacting with the macroscopic world components which are modeled by collections of bosonic modes. The interaction is via a general operator $Λ$ of the system, coupled to the creation and annihilation operators of the environment modes. We assume that in the process of a nearly instantaneous quantum measurement, the function of the environment involves two distinct parts: the pointer and the bath. Interaction of the system with the bath leads to decoherence such that the system and the pointer both evolve into a statistical mixture state described by the density matrix such that the system is in one of the eigenstates of $Λ$ with the correct quantum mechanical probability, whereas the expectation values of pointer operators retain amplified information on that eigenstate. We argue that this process represents the initial step of a quantum measurement. Calculation of the elements of the reduced density matrix of the system and pointer is carried out exactly, and time dependence of decoherence is identified. We discuss general implications of our model of energy-conserving coupling to a heat bath for processes of adiabatic quantum decoherence. We also evaluate changes in the expectation values of certain pointer operators and suggest that these can be interpreted as macroscopic indicators of the measurement outcome.

quant-ph↗
arXiv2000

Recent Theoretical Results for Nonequilibrium Deposition of Submicron Particles

Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We review deposition processes involving extended objects, with jamming and its interplay with in-surface diffusion yielding interesting dynamics of approach to the large-time state. Mean-field and low-density approximation schemes can be used in many instances for short and intermediate times, in large enough dimensions, and for particle sizes larger than few lattice units. Random sequential adsorption models are appropriate for higher particle densities (larger times). Added diffusion allows formation of denser deposits and leads to power-law large-time behavior which, in one dimension (linear substrate, such as DNA), was related to diffusion-limited reactions, while in two dimensions (planar substrate), was associated with evolution of the domain-wall and defect network, reminiscent of equilibrium ordering processes.

cond-mat.mtrl-sci↗
arXiv2000

Growth of Monodispersed Colloids by Aggregation of Nucleating Subunits

Formation of monodispersed colloidal particles is a complex process: nuclei, produced rapidly in a supersaturated solution, grow to nanosize primary particles, which then aggregate (coagulate) to form much larger final colloids. This paper reviews a kinetic model that explains the formation of dispersions of narrow size distribution in such processes. Numerical simulations of the kinetic equations, with experimental model parameter values, are reported. The model was tested for a system involving formation of uniform spherical gold particles. The calculated average size, the width of the particle size distribution, and the time scale of the process, agreed semiquantitatively with the experimental values.

cond-mat.mtrl-sci↗
arXiv2000

Measurement of a Quantum System Coupled to Independent Heat-Bath and Pointer Modes

We present an exact derivation of a process in which a microscopic measured system interacts with heat-bath and pointer modes of a measuring device, via a coupling involving a general Hermitian operator $Λ$ of the system. In the limit of strong interaction with these modes, over a small time interval, we derive the exact effective many-body density matrix of the measured system plus pointer. We then discuss the interpretation of the dynamics considered as the first stage in the process of quantum measurement, eventually involving the wave-function collapse due to interactions with "the rest of the universe." We establish that the effective density matrix represents the required framework for the measured system and the pointer part of the measuring device to evolve into a statistical mixture described by direct-product states such that the system is in each eigenstate of $Λ$ with the correct quantum-mechanical probability, whereas the expectation values of pointer-space operators retain amplified information of the system's eigenstate.

cond-mat.mes-hall↗
arXiv1999

Dynamics of Nonequilibrium Deposition

In this work we survey selected theoretical developments for models of deposition of extended particles, with and without surface diffusion, on linear and planar substrates, of interest in colloid, polymer, and certain biological systems.

cond-mat.mtrl-sci↗
arXiv1998

Diffusional Growth of Colloids

We consider incorporation of particle detachment in Smoluchowski model of colloidal growth. Two approaches are considered, utilizing phenomenological rate equation and exact large-time results. Our main conclusion is that the value of the large-time diffusing particle concentration at the aggregate surface is the only parameter needed to describe the added effect of detachment. Explicit expression is given for the particle intake rate.

cond-mat.mtrl-sci↗
arXiv1998

Mechanism of Formation of Monodispersed Colloids by Aggregation of Nanosize Precursors

It has been experimentally established in numerous cases that precipitation of monodispersed colloids from homogeneous solutions is a complex process. Specifically, it was found that in many systems nuclei, produced rapidly in a supersaturated solution, grow to nanosize primary particles (singlets), which then coagulate to form much larger final colloids in a process dominated by irreversible capture of these singlets. This paper describes a kinetic model that explains the formation of dispersions of narrow size distribution in such systems. Numerical simulations of the kinetic equations, with experimental model parameter values, are reported. The model was tested for a system involving formation of uniform spherical gold particles by reduction of auric chloride in aqueous solutions. The calculated average size, the width of the particle size distribution, and the time scale of the process, agreed reasonably well with the experimental values.

cond-mat.mtrl-sci↗
arXiv1997

Design of gates for quantum computation: the NOT gate

We offer an alternative to the conventional network formulation of quantum computing. We advance the analog approach to quantum logic gate/circuit construction. As an illustration, we consider the spatially extended NOT gate as the first step in the development of this approach. We derive an explicit form of the interaction Hamiltonian corresponding to this gate and analyze its properties. We also discuss general extensions to the case of certain time-dependent interactions which may be useful for practical realization of quantum logic gates.

quant-ph↗
arXiv1997

Quantum signal splitting that avoids initialization of the targets

The classical signal splitting and copying are not possible in quantum mechanics. Specifically, one cannot copy the basis up and down states of the input (I) two-state system (qubit, spin) into the copy (C) and duplicate-copy (D) two-state systems if the latter systems are initially in an arbitrary state. We consider instead a quantum evolution in which the basis states of I at time t are duplicated in at least two of the systems I, C, D, at time t + Delta t. In essence, the restriction on the initial target states is exchanged for uncertainty as to which two of the three qubits retain copies of the initial source state.

quant-ph↗
arXiv1997

Three-Species Diffusion-Limited Reaction with Continuous Density-Decay Exponents

We introduce a model of three-species two-particle diffusion-limited reactions A+B -> A or B, B+C -> B or C, and C+A -> C or A, with three persistence parameters (survival probabilities in reaction) of the hopping particle. We consider isotropic and anisotropic diffusion (hopping with a drift) in 1d. We find that the particle density decays as a power-law for certain choices of the persistence parameter values. In the anisotropic case, on one symmetric line in the parameter space, the decay exponent is monotonically varying between the values close to 1/3 and 1/2. On another, less symmetric line, the exponent is constant. For most parameter values, the density does not follow a power-law. We also calculated various characteristic exponents for the distance of nearest particles and domain structure. Our results support the recently proposed possibility that 1d diffusion-limited reactions with a drift do not fall within a limited number of distinct universality classes.

cond-mat.stat-mech↗
arXiv1997

Hamiltonians for Quantum Computing

We argue that the analog nature of quantum computing makes the usual design approach of constructing complicated logical operations from many simple gates inappropriate. Instead, we propose to design multi-spin quantum gates in which the input and output two-state systems (spins) are not necessarily identical. We outline the design criteria for such devices and then review recent results for single-unit Hamiltonians that accomplish the NOT and XOR functions.

quant-ph↗