Random quantum states: recent developments and applications

We examine the statistical properties of a pure quantum state randomly chosen with respect to the uniform measure in a Hilbert space. Namely, we consider the distribution of outcomes of a fixed measurement performed on the random quantum state. We show that such distribution is completely analogous to the distribution of measurement outcomes of an a priori unknown classical random system. In particular, Shannon entropies of both distributions coincide. We study this correspondence between quantum and classical random systems and clarify its origin.

We define quantum chaos and integrability in open quantum many-body systems as a dynamical property of single stochastic realizations, referred to as quantum trajectories. This definition relies on the predictions of random matrix theory applied to the subset of the Liouvillian eigenspectrum involved in each quantum trajectory. Our approach, which we name (SSQT), enables a natural distinction between transient and steady-state quantum chaos as general phenomena in open setups. We test the generality and reliability of the SSQT criterion on several dissipative systems, further showing that an open system with a chaotic structure can evolve towards either a chaotic or integrable steady state. We apply our theoretical framework to two driven-dissipative bosonic systems. First, we study the driven-dissipative Bose-Hubbard model, a paradigmatic example of a quantum simulator, clarifying the interplay of integrability, transient, and steady-state chaos across its phase diagram. Our analysis shows the existence of an emergent dissipative quantum chaotic phase, whereas the classical and semiclassical limits display an integrable behavior. In this regime, chaos arises from the quantum and classical fluctuations associated with the dissipation mechanisms. Second, we investigate dissipative quantum chaos in the dispersive readout of a transmon qubit: a measurement technique ubiquitous in superconducting-based quantum hardware. Through the SSQT, we distinguish several regimes where the performance of the measurement instrument can be connected to the integrable or chaotic nature of the underlying driven-dissipative bosonic system. Our work offers a general understanding of the integrable and chaotic dynamics of open quantum systems and paves the way for the investigation of dissipative quantum chaos and its consequences on state-of-the-art noisy intermediate-scale quantum devices.

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

The chapter reviews the recent technology developments and applications of NMR in industry from 2015 to middle 2019. The chapter is divided into sections focused on applications of hyphenated NMR as a continuation of the review article published in 2016, expanding the areas of low and high field NMR for process monitoring, and including sections on specific examples for the application of solid state NMR in the pharmaceutical industry, other applications on low field NMR beyond process monitoring, contributions on NMR in the pharmaceutical, food and petroleum industry, relative configuration of molecules by NMR, and recent magnet technology development.

Quantum chaos and interference

When a quantum system is divided into two local subsystems, measurements on the two subsystems can exhibit correlations beyond those possible in a classical joint probability distribution; these are partially explained by entanglement, and more generally by a wider class of measures such as the quantum discord. In this paper, I introduce a simple thought experiment defining a measure of quantum correlations, which I call the accord, and write the result as a minimax optimization over unitary matrices. I find the exact result for pure states as a simple function of the Schmidt coefficients and provide a complete proof, and I likewise provide and prove the result for several classes of mixed states, notably including all states of two qubits and the experimentally relevant case of a pure state mixed with colorless noise. I demonstrate that for two qubit states the accord provides a tight lower bound on the discord; for Bell diagonal states it is also an upper bound on entanglement.

Fermions from classical statistics

ABSTRACT: In this paper, an overview on the mechanisms, techniques and applications of the vacuum preloading method are presented. Some recent developments in the vacuum preloading techniques, including the use of new materials, the expansion of the method, and new analysis or numerical modeling methods are briefly summarized. INTRODUCTION It has been 56 years since the idea of vacuum preloading was proposed by Kjellman (1952). Since then, the vacuum preloading method has evolved into a mature and efficient technique for the treatment of soft clay. This method has been successfully used for soil improvement or land reclamation projects in a number of countries (Holtz 1975; Chen and Bao 1983; Bergado et al. 1998; Chu et al. 2000; Indraratna et al. 2005). With the merging of new materials and new technologies, this method has been further improved in recent years. A brief overview of this technique and the recent developments and applications is given in this paper. In adopting this technique, sand drains and recently prefabricated vertical drains (PVDs) have often been used to distribute the vacuum pressure and discharge pore water. A nominal vacuum load of 80 kPa is normally used in design although a higher vacuum pressure of up to 90 kPa may be achieved sometimes. When a surcharge load higher than 80 kPa is required, a combined vacuum and fill surcharge can be applied. For the treatment of very soft ground, the vacuum preloading method is faster than the fill surcharge method, as the 80 kPa vacuum pressure can be applied almost instantly, without causing stability problem. The vacuum preloading method is also cheaper when compared with the fill surcharge method for an equivalent load (Chu et al. 2000). The vacuum preloading method has also been incorporated in the land reclamation process when clay slurry dredged from seabed is used as fill material for land reclamation. As the clay slurry fill is too soft for fill surcharge to be applied, the vacuum preloading method is ideally used for the consolidation of the clay slurry. Thousands of hectares of land have been

The study of open quantum systems is important for fundamental issues of quantum physics as well as for technological applications such as quantum information processing. Recent developments in this field have increased our basic understanding on how non-Markovian effects influence the dynamics of an open quantum system, paving the way to exploit memory effects for various quantum control tasks. Most often, the environment of an open system is thought to act as a sink for the system information. However, here we demonstrate experimentally that a photonic open system can exploit the information initially held by its environment. Correlations in the environmental degrees of freedom induce nonlocal memory effects where the bipartite open system displays, counterintuitively, local Markovian and global non-Markovian character. Our results also provide novel methods to protect and distribute entanglement, and to experimentally quantify correlations in photonic environments.

Using Liouville space and superoperator formalism we consider pure stationary states of open and dissipative quantum systems. We discuss stationary states of open quantum systems, which coincide with stationary states of closed quantum systems. Open quantum systems with pure stationary states of linear oscillator are suggested. We consider stationary states for the Lindblad equation. We discuss bifurcations of pure stationary states for open quantum systems which are quantum analogs of classical dynamical bifurcations.

Fractional Brownian Motions, Fractional Noises and Applications

In a previous essay I argued that quantum chaos cannot be exhibited in models of quantum systems within von Neumann's mathematical framework for quantum mechanics, and that it can be exhibited in models within Dirac's formal framework. In this essay, the negative thesis concerning von Neumann's framework is elaborated further by extending it to the case of Hamiltonian operators having a continuous spectrum. The positive thesis concerning Dirac's formal framework is also elaborated further by constructing a chaotic model of an open quantum system in which an entropy measure is shown to approach its maximum value as time goes to infinity. Having such an entropy measure is a characteristic that is closely connected to chaotic behavior in phase space models of classical systems.

The deficiencies existing in Geotechnical parameters distribution fitting using the classical probability distribution are analyzed and the stochastic weighting method is employed to improve the the small samples of Geotechnical parameters into big samples, thus sloving the problems caused by the small sample. The maximum entropy principle and the big samples improving from small sample are used to generate probability density functions of Geotechnical parameters. It is more rational and scientific with the method proposed in the paper through the Kolmogorov-Smirnov Test. It is demonstrated through the example that the method presented in this paper not only successfully escapes the reliance of the classical probability distribution functions, but also make the computation result more closed to the fact due to the data coming from the big sample improving from the small sample, which has important engineering significance.

The properties of an ideal gas of spinless particles are investigated by using the path integral formalism. It is shown that the quantum paths exhibit a fractal character which remains unchanged in the relativistic domain provided the creation of new particles is avoided, and the Brownian motion remains the stochastic process associated with the quantum paths. These results are obtained by using a special representation of the Klein-Gordon wave equation. On the quantum paths the relation between velocity and momentum is not the usual one. The mean square value of the velocity depends on the time needed to define the velocity and its value shows the interplay between pure quantum effects and thermodynamics. The fractal character is also investigated starting from wave equations by analyzing the evolution of a Gaussian wave packet via the Hausdorff dimension. Both approaches give the same fractal character in the same limit. It is shown that the time that appears in the path integral behaves like an ordinary time, and the key quantity is the time interval needed for the thermostat to give to the particles a thermal action equal to the quantum of action. Thus, the partition function calculated via the path integral formalism also describes the dynamics of the system for short time intervals. For low temperatures, it is shown that a time-energy uncertainty relation is verified at the end of the calculations. The energy involved in this relation has not a thermodynamic meaning but results from the fact that the particles do not follow the equations of motion along the paths. The results suggest that the density matrix obtained by quantification of the classical canonical distribution function via the path integral formalism should not be totally identical to that obtained via the usual route.

As a new generation of stationary phases, monolithic supports have attracted significant interest in high-performance liquid chromatography (HPLC) and capillary electrochromatography (CEC) because of their ease of preparation, high reproducibility, versatile surface chemistry and rapid mass transport. Molecularly imprinted polymers (MIPs) are synthetic materials with high specific recognition ability to template molecule. The combination of monolithic column and MIPs integrates the high efficiency of modern chromatography and the high selectivity provided by MIPs. This review focuses on the recent developments and applications of all kinds of monolithic matrix, i.e. organic polymer-based and silica-based MIP monolith in HPLC and CEC mode.