Showing papers on "Quantum evolution published in 2016"

Mean‐Field Evolution of Fermionic Mixed States

Abstract: In this paper we study the dynamics of fermionic mixed states in the mean-field regime. We consider initial states that are close to quasi-free states and prove that, under suitable assumptions on the initial data and on the many-body interaction, the quantum evolution of such initial data is well approximated by a suitable quasi-free state. In particular, we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent Hartree-Fock equation. Our result holds for all times and gives effective estimates on the rate of convergence of the many-body dynamics towards the Hartree-Fock evolution.© 2015 Wiley Periodicals, Inc.

Generalized Pauli channels and a class of non-Markovian quantum evolution

Abstract: We analyze the quantum evolution represented by a time-dependent family of generalized Pauli channels. This evolution is provided by the random decoherence channels with respect to the maximal number of mutually unbiased bases. We derive the necessary and sufficient conditions for the vanishing back-flow of information.

Exponential Sensitivity and its Cost in Quantum Physics.

Abstract: State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrodinger microscope) is possible; however, there is a strict bound on the number of copies needed.

Geometry of a two-spin quantum state in evolution

Abstract: We study the quantum evolution of a two-spin system described by the isotropic Heisenberg Hamiltonian in the external magnetic field. It is shown that this evolution happens on a two-parametric closed manifold. The Fubini–Study metric of this manifold is obtained. It is found that this is the metric of the torus. The entanglement of the states which belong to this manifold is investigated.

Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator

Abstract: A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to resolve the classical dynamics and the quantum evolution in order to understand the time-dependent phenomena that occur not only in the macroscopic classical scale for the synchronized behaviors but also in the microscopic quantum scale for a coherent state evolution. By using a Floquet U-transformation on a general time-dependent quadratic Hamiltonian, we exactly solve the dynamic behaviors of a driven and damped parametric oscillator to obtain the optimal solutions by means of invariant parameters of $K$s to combine with Lewis-Riesenfeld invariant method. This approach can discriminate the external dynamics from the internal evolution of a wave packet by producing independent parametric equations that dramatically facilitate the parametric control on the quantum state evolution in a dissipative system. In order to show the advantages of this method, several time-dependent models proposed in the quantum control field are analyzed in details.

Markov constant and quantum instabilities

Abstract: For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept of Markov constant known in Diophantine approximation theory) are shown to provide a new mathematical insight in the phenomenologically relevant occurrence of anomalies in the spectra. Our results may inspire methodical innovations ranging from the description of the stability properties of metamaterials and of certain hiddenly unitary quantum evolution models up to the clarification of the mechanisms of occurrence of ghosts in quantum cosmology.

Quantum Theory on Genome Evolution

Abstract: A model of genome evolution is proposed. Based on several general assumptions the evolutionary theory of a genome is formulated. Both the deterministic classical equation and the stochastic quantum equation are proposed. The classical equation is written in a form of of second-order differential equations on nucleotide frequencies varying in time. It is proved that the evolutionary equation can be put in a form of the least action principle and the latter can be used for obtaining the quantum generalization of the evolutionary law. The wave equation and uncertainty relation for the quantum evolution are deduced logically. Two fundamental constants of time dimension, the quantization constant and the evolutionary inertia, are introduced for characterizing the genome evolution. During speciation the large-scale rapid change of nucleotide frequency makes the evolutionary inertia of the dynamical variables of the genome largely decreasing or losing. That leads to the occurrence of quantum phase of the evolution. The observed smooth/sudden evolution is interpreted by the alternating occurrence of the classical and quantum phases. In this theory the probability of new-species formation is calculable from the first-principle. To deep the discussions we consider avian genome evolution as an example. More concrete forms on the assumed potential in fundamental equations, namely the diversity and the environmental potential, are introduced. Through the numerical calculations we found that the existing experimental data on avian macroevolution are consistent with our theory. Particularly, the law of the rapid post-Cretaceous radiation of neoavian birds can be understood in the quantum theory. Finally, the present work shows the quantum law may be more general than thought, since it plays key roles not only in atomic physics, but also in genome evolution.

Combinatorial Approach to Modeling Quantum Systems

Abstract: Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers and unitarity in the formalism of the quantum mechanics. In our approach, the quantum behavior can be explained by the fundamental impossibility to trace the identity of the indistinguishable objects in their evolution. Any observation only provides information about the invariant relations between such objects.The trajectory of a quantum system is a sequence of unitary evolutions interspersed with observations—non-unitary projections. We suggest a scheme to construct combinatorial models of quantum evolution. The principle of selection of the most likely trajectories in such models via the large numbers approximation leads in the continuum limit to the principle of least action with the appropriate Lagrangians and deterministic evolution equations

Manifestations of classical physics in the quantum evolution of correlated spin states in pulsed NMR experiments

Abstract: Multiple-pulse NMR experiments are a powerful tool for the investigation of molecules with coupled nuclear spins. The product operator formalism provides a way to understand the quantum evolution of an ensemble of weakly coupled spins in such experiments using some of the more intuitive concepts of classical physics and semi-classical vector representations. In this paper I present a new way in which to interpret the quantum evolution of an ensemble of spins. I recast the quantum problem in terms of mixtures of pure states of two spins whose expectation values evolve identically to those of classical moments. Pictorial representations of these classically evolving states provide a way to calculate the time evolution of ensembles of weakly coupled spins without the full machinery of quantum mechanics, offering insight to anyone who understands precession of magnetic moments in magnetic fields.

Accurate switching currents measurements in quantum washboard potential

Abstract: We tackle the problem of accurate simulations of switching currents arising from tunnel events in the washboard potentials associated to Josephson junctions. The measurements of the probability distribution of the switching currents is essential to determine the quantum character of the device, and therefore is at the core of technological applications, as Josephson junctions, that have been proposed for quantum computers. In particular, we show how to accurately calibrate the parameters of the boundary conditions to avoid spurious reflections of the wavefunction from the finite border of numerical simulations. The proposed approximate numerical scheme exploits a quantum version of a prefect matched layers for the boundary problems associated with this class of potentials. Thus, we employ the analogous of a well established electromagnetic method to deal with radiation in mesoscopic quantum systems. Numerical simulations demonstrate that the known analytic results are well recovered in the appropriated limits of quantum measurements. We also find that a relaxation time shows up in the dynamics of the quantum evolution in between two consecutive measurements.

Spectrum sensing method based on multi-target quantum glowworm searching mechanism

Abstract: The invention provides a spectrum sensing method based on a multi-target quantum glowworm searching mechanism. The method comprises the steps that a multi-target spectrum sensing model is built, and parameters of a searching method are determined; a form of a multi-target fitness function needing to be solved is determined; non-dominated quantum position sorting is conducted on quantum positions of quantum glowworms in population according to fitness values of the quantum positions, and the quantum positions, of which the non-dominated level is 1, of the quantum glowworms are put into an elite quantum position set; the quantum positions of the quantum glowworms are updated by using a quantum coding mechanism and a quantum evolution behavior, non-dominated quantum positions are selected, and the elite quantum position set is updated; according to the final Pareto front-end quantum position set, a cognitive radio system selects a corresponding quantum position according to the different requirements of the maximized detection probability and the minimized false alarm probability. According to the spectrum sensing method based on the multi-target quantum glowworm searching mechanism, the technical problem of multi-target spectrum sensing can be solved, and the spectrum sensing method can be applied to some scenes to which an existing cognitive radio spectrum sensing method cannot be applied.

Time-symmetrized description of nonunitary time asymmetric quantum evolution

Abstract: We discuss how systems which evolve manifestly asymmetrically in time can be described within the framework of the time-symmetrized quantum mechanics. An obvious case of asymmetry arises when a pure state evolves into a mixed state via effectively non-unitary evolution. A two-state method for finding the intermediate probability in postselected systems under such evolution is developed and the time-symmetry aspects of the method are explicitly considered. A specific feature is the existence of the so-called second scenario in which the state originating from the postselection measurement evolves under different evolution superoperator than the state from the preselection measurement. The evolution of the second scenario is explicitly defined. We illustrate the method with two characteristic examples: the spontaneous deexcitation of atoms and the systems approaching thermal equilibrium. We consider the systems with two energy levels and calculate the time-symmetrized probability of finding the system in excited state, under general preselection and postselection conditions. The consequences of the asymmetry of the time evolution on this probability are discussed. It is demonstrated that the arrow of time can be reconstructed in some special cases of postselected systems, while, for a general system, this is not the case.