Search results for "STATES"
showing 10 items of 1532 documents
Empirical investigation of stock price dynamics in an emerging market
1999
Abstract We study the development of an emerging market – the Budapest Stock Exchange – by investigating the time evolution of some statistical properties of heavily traded stocks. Moving quarter by quarter over a period of two and a half years we analyze the scaling properties of the standard deviation of intra-day log-price changes. We observe scaling using both seconds and ticks as units of time. For the investigated stocks a Levy shape is a good approximation to the probability density function of tick-by-tick log-price changes in each quarter: the index of the distribution follows an increasing trend, suggesting it could be used as a measure of market efficiency.
Bi-squeezed states arising from pseudo-bosons
2018
Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the \emph{bi-squeezed states}, and we deduce their main mathematical properties. We relate bi-squeezed states to the so-called regular and non regular pseudo-bosons. We show that these two cases are different, from a mathematical point of view. Some physical examples are considered.
Coherent states: a contemporary panorama
2012
Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schr?dinger in answer to a remark by Lorentz on the classical interpretation of the wave function. They were rediscovered in the early 1960s, first (somewhat implicitly) by Klauder in the context of a novel representation of quantum states, then by Glauber and Sudarshan for the description of coherence in lasers. Since then, CS have grown into an extremely rich domain that pervades almost every corner of physics and have also led to the development of several flourishing topics in mathematics. Along the way, a number of review articles have appeared in the literature, devoted to CS, notably…
Some results on the rotated infinitely deep potential and its coherent states
2021
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is because the Swanson Hamiltonian is deeply connected with that of a standard quantum Harmonic oscillator, after a suitable rotation in configuration space is performed. In this paper we consider a rotated version of a different quantum system, the infinitely deep potential, and we consider some of the consequences of this rotation. In particular, we show that differences arise with respect to the Swanson model, mainly because of the technical need of working, he…
New trends in nonequilibrium statistical mechanics: classical and quantum systems
2020
The main aim of this special issue is to report recent advances and new trends in nonequilibrium statistical mechanics of classical and quantum systems, from both theoretical and experimental points of view, within an interdisciplinary context. In particular, the nonlinear relaxation processes in the dynamics of out-of-equilibrium systems and the role of the metastability and environmental noise will be overviewed. Three main areas of nonequilibrium statistical mechanics will be covered: slow relaxation phenomena and dissipative dynamics; long-range interactions and classical systems; quantum systems. New trends such as quantum thermodynamics and novel types of quantum phase transitions occ…
Electron Fabry-Perot interferometer with two entangled magnetic impurities
2007
We consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron-impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave vectors, the triplet and singlet maximally entangled spin states of the impurities can respectively…
Unitary Representations of Quantum Superpositions of two Coherent States and beyond
2013
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad hoc introduced set of hermitian operators, leads to the definition of new basis in the oscillator Hilbert space, extending in a natural way the displaced Fock states basis. The potential development of our method and our results are briefly outlined.
A Swanson-like Hamiltonian and the inverted harmonic oscillator
2022
We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian $H_\theta$ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the eigensystem of the Hamiltonian $H$ of the inverted quantum harmonic oscillator can be deduced from that of $H_\theta$. We show that there is no need to introduce a different scalar product using some ad hoc metric operator, as suggested by other authors. Indeed we prove that a distributional approach is sufficient to deal with the Hamiltonian $H$ of the inverted oscillator.
Newton algorithm for Hamiltonian characterization in quantum control
2014
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown paramete…
A multi-scale approach for testing and detecting peaks in time series
2020
An approach is presented that combines a statistical test for peak detection with the estimation of peak positions in time series. Motivated by empirical observations in neuronal recordings, we aim at investigating peaks of different heights and widths. We use a moving window approach to compare the differences of estimated slope coefficients of local regression models. We combine multiple windows and use the global maximum of all different processes as a test statistic. After rejection, a multiple filter algorithm combines peak positions estimated from multiple windows. Analysing neuronal activity recorded in anaesthetized mice, the procedure could identify significant differences between …