Quadratic Quantum Measurements

We develop a theory of quadratic quantum measurements by a mesoscopic detector. It is shown that quadratic measurements should have non-trivial quantum information properties, providing, for instance, a simple way of entangling two non-interacting qubits. We also calculate output spectrum of a quantum detector with both linear and quadratic response continuously monitoring coherent oscillations in two qubits.Comment: 5 pages, 2 figure

Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond

Recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. We discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson's orthogonality catastrophe (OC), which could not be accessed in solid state systems. We consider a system of impurity atoms localized by a strong optical lattice potential and immersed in a sea of itinerant Fermi atoms. Ramsey interference experiments with impurity atoms probe OC in the time domain, while radio-frequency (RF) spectroscopy probes OC in the frequency domain. The OC in such systems is universal for all times and is determined by the impurity scattering length and Fermi wave vector of itinerant fermions. We calculate the universal Ramsey response and RF absorption spectra. In addition to the standard power-law contribution, which corresponds to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel contribution to OC that comes from exciting one extra particle from the bottom of the itinerant band. This gives rise to a non-analytic feature in the RF absorption spectra, which evolves into a true power-law singularity with universal exponent 1/4 at the unitarity. Furthermore, we discuss the manifestations of OC in spin-echo experiments, as well as in the energy counting statistic of the Fermi gas following a sudden quench of the impurity state. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying non-equilibrium impurity physics, allowing one to explore non-equilibrium OC and to simulate quantum transport through nano-structures. This provides a useful connection between cold atomic systems and mesoscopic quantum transport.Comment: 15 pages, 7 figure

Mathematical modeling of virtual machine life cycle using branching renewal process

In this paper, we propose the branching renewal process as a model of virtual machine life cycle in cloud node. We assume that virtual machines have several working modes with different resource consumption. Each machine begins with zero phase and continues performing by probabilistic change of other phases. Virtual machines can leave the cloud node after any phase with some probability. For this model, we obtain probability distribution of the number of simultaneously performing virtual machines in each phase and the distribution function of resource consumption in cloud node

Queueing system with two phases of service and service rate degradation

In the paper, a queueing system with an unlimited number of servers and two phases of service with degradation in the service rate is studied. The problem of service rate degradation emerges in cloud nodes, where there is contention for hardware resources including computational resources such as CPU cores. In a node, we have a limited number of CPU cores that should execute potentially an unlimited number of processes (requests) in parallel. In our model, the term “server” means a process allocated in the node for execution. So, the number of “servers” is unlimited but their individual performances decrease because CPUs should switch between them during the execution. We consider processes executed in the node with two phases of life cycle that reflects periods with different activity of a process; e.g., in the first phase, the process may require intensive usage of CPU cores but low usage in the second one. Our model distinguishes the phases using different service parameters for them as well as different influence on the service rate degradation in the node. In the paper, two analytical methods are proposed: exact solving of the system of the local balance equation and the asymptotic analysis of the global balance equations. Formulas for the stationary probability distribution of the number of customers in the phases are obtained for both cases. Several numerical examples are provided that illustrate some properties and applicability of the obtained results

Spin relaxation in semiconductor quantum dots

We have studied the physical processes responsible for the spin -flip in GaAs quantum dots. We have calculated the rates for different mechanisms which are related to spin-orbit coupling and cause a spin-flip during the inelastic relaxation of the electron in the dot both with and without a magnetic field. We have shown that the zero-dimensional character of the problem when electron wave functions are localized in all directions leads to freezing out of the most effective spin-flip mechanisms related to the absence of the inversion centers in the elementary crystal cell and at the heterointerface and, as a result, to unusually low spin-flip rates.Comment: 6 pages, RevTe

Mathematical model of Scheduler with Semi-Markov input and bandwidth sharing discipline

In this paper, we consider single server queueing system with multiple semi-Markov inputs and buffers. Each request of the flows brings to the system some random amount of information. According to the bandwidth sharing discipline, each buffer has its own part of the throughput and the server transmits the information from buffers simultaneously. The aim of the current research is to derive the probability distribution of the amount of information in single buffer

Real waiting time in single-server resource queue with Markovian arrival process

We consider single-server queue, which models a telecommunication node. Packets arrive in the system according to the Markovian arrival process (MAP). The packets bring some amount of information, which is stored in a continuous-type unlimited buffer before it will be transmitted out of the system. We consider the system with fluid manner of service, which means that the server takes the information from the buffer with constant speed. Our aim is to derive the probability distribution of the real waiting time in the syste

On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^N

In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of \Co^{N}. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in \Co^{2}.Comment: minor changes in the formulation and the proof of Lemma 8.

Semi-Markov resource flow as a bit-level model of traffic

In this paper, we consider semi-Markov flow as a bit-level model of traffic. Each request of the flow brings some arbitrary distributed amount of information to the system. The current paper aims to investigate the amount of information received in semi-Markov flow during time unit. We use the asymptotic analysis method under the limit condition of growing time of observation to derive the limiting probability distribution of the amount of information received in the flow and build the approximation of its prelimit distribution function

Conductance fluctuations in mesoscopic normal-metal/superconductor samples

We study the magnetoconductance fluctuations of mesoscopic normal-metal/superconductor (NS) samples consisting of a gold-wire in contact with a niobium film. The magnetic field strength is varied over a wide range, including values that are larger than the upper critical field B_c2 of niobium. In agreement with recent theoretical predictions we find that in the NS sample the rms of the conductance fluctuations (CF) is by a factor of 2.8 +/- 0.4 larger than in the high field regime where the entire system is driven normal conducting. Further characteristics of the CF are discussed.Comment: 4 pages, REVTEX, 3 eps-figures included. To be published in Phys. Rev. Lett.. Changes: one misplaced figure correcte