Numerical approaches to time evolution of complex quantum systems

We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev polynomials. The Chebyshev approach benefits from two advantages over the standard time-integration Crank-Nicholson scheme: speedup and efficiency. Potential competitors are semiclassical methods such as the Wigner-Moyal or quantum tomographic approaches. We outline the basic concepts of these techniques and benchmark their performance against the Chebyshev approach by monitoring the time evolution of a Gaussian wave packet in restricted one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes and the motion in anharmonic potentials. Finally we apply the prominent Chebyshev technique to two highly non-trivial problems of current interest: (i) the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the spatiotemporal evolution of polaron states in finite quantum systems. Here, depending on the disorder/electron-phonon coupling strength and the device dimensions, we observe transmission or localisation of the matter wave.Comment: 8 pages, 3 figure

The physics and applications of strongly coupled plasmas levitated in electrodynamic traps

Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coulomb systems, which are the subject of current investigation. Exciting physical phenomena associated to Coulomb systems have been reported such as autowave generation, phase transitions, system self-locking at the ends of the linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged nanoparticles, with coupling parameter of the order $\Gamma = 10^8$ is investigated. This approach enables us to study the interaction of nanoparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces these structures experience. Applications of electrodynamic levitation for mass spectrometry, including containment and study of single aerosols and nanoparticles are reviewed, with an emphasis on state of the art experiments and techniques, as well as future trends. Late experimental data suggest that inelastic scattering can be successfully applied to the detection of biological particles such as pollen, bacteria, aerosols, traces of explosives or synthetic polymers. Brownian dynamics is used to characterize charged particle evolution in time and thus identify regions of stable trapping. An analytical model is used to explain the experimental results. Numerical simulations take into account the stochastic forces of random collisions with neutral particles, the viscosity of the gas medium, the regular forces produced by the a.c. trapping voltage, and the gravitational force. We show that microparticle dynamics is characterized by a stochastic Langevin differential equation. Laser plasma acceleration of charged particles is also discussed

Редкий случай верхушечной формы гипертрофической кардиомиопатии с внутрижелудочковой обструкцией у ребенка

Hypertrophic cardiomyopathy is characterized by primary hypertrophy of myocardium without another cause such as arterial hypertension. We present a rare case of apical hypertrophic cardiomyopathy in 7-year-old girl with minimal nonspecific clinical manifestation (headache after loading). At planned examination typically ECG changes - pronounced repolarization changes and deep (about 10 mm) inverted T waves in precordial leads - were discovered. Transthoracic echocardiography detected local symmetric hypertrophy of left ventricular apex with reduced contractility of this area and intraventricular obstruction with pressure gradient between apical and middle parts of left ventricle 30 mm Hg. This findings were confirmed by ventriculograhy and myocardial scintigraphy. Cardiac magnetic resonance imaging determined marked fibrotic transformation of left ventricular apex. The features of this case are: the young age of the patient and combination of apical hypertrophy with intraventricular obstruction.Гипертрофическая кардиомиопатия характеризуется первичной гипертрофией миокарда при отсутствии других причин этого, в частности артериальной гипертензии. Представлен редкий случай верхушечной гипертрофической кардиомиопатии у девочки 7 лет с минимальными неспецифическими клиническими проявлениями (головные боли, провоцируемые нагрузками). При плановом обследовании были обнаружены типичные изменения на ЭКГ - выраженные нарушения реполяризации миокарда и глубокие (до 10 мм) отрицательные зубцы Т в грудных отведениях. Трансторакальная эхокардиография выявила локальную симметричную гипертрофию верхушечных отделов левого желудочка с нарушением их сократимости и внутрижелудочковую обструкцию с градиентом давления между верхушечным и средним отделами 30 мм рт.ст., что было подтверждено данными вентрикулографии и сцинтиграфии миокарда. МРТ сердца позволила установить наличие выраженной фиброзной трансформации верхушки левого желудочка. Особенностью данного случая являются детский возраст пациентки и сочетание верхушечной гипертрофии миокарда с внутрижелудочковой обструкцией

Quantum Dynamics of Charged Fermions in the Wigner Formulation of Quantum Mechanics

To study the kinetic properties of dense quantum plasma, a new quantum dynamics method in the Wigner representation of quantum mechanics has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. This method combines the Feynman and Wigner formulation of quantum mechanics and uses for calculation the path integral Monte-Carlo (WPIMC) in phase space and quantum generalization of the classical molecular dynamics methods (WMD) allowing to solve the quantum Wigner⁻Liouville-like equation. The Fermi⁻Dirac statistical effects are accounted for by the effective pair pseudopotential depending on coordinates and momenta and allowing to avoid the famous “sign problem„ due to realization of the Pauli blocking of fermions. Significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions have been observed. According to the quantum Kubo formula, we also study the electron conductivity of dense plasma media

Quantum statistics of dense gases and nonideal plasmas

The aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter – ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of the visible Universe is in the state of gases and plasmas and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interior of stars. This text, combining material from lectures and advanced seminars given by the authors over many decades, is a must-have introduction and reference for both newcomers and seasoned researchers alike

Momentum Distribution Functions and Pair Correlation Functions of Unpolarized Uniform Electron Gas in Warm Dense Matter Regime

In this paper we continued our research of the uniform electron gas in a warm dense matter regime, focusing on the momentum distribution functions and pair correlation functions. We use the single–momentum path integral Monte Carlo method, based on the Wigner formulation of quantum statistics to calculate both momentum- and coordinate-depending distributions and average values of quantum operators for many-fermion Coulomb systems. We discovered that the single-particle momentum distribution function deviates from the ideal Fermi distribution and forms the so-called “quantum tails” at high momenta, if non-ideality is strong enough in both degenerate and non-degenerate cases. This effect is always followed by the appearance of the short-range order on pair correlation functions and can be explained by the tunneling through the effective potential wells surrounding the electrons. Furthermore, we calculated the average kinetic and potential energies in the wide range of states, expanding our previous results significantly

Momentum Distribution Functions and Pair Correlation Functions of Unpolarized Uniform Electron Gas in Warm Dense Matter Regime

In this paper we continued our research of the uniform electron gas in a warm dense matter regime, focusing on the momentum distribution functions and pair correlation functions. We use the single–momentum path integral Monte Carlo method, based on the Wigner formulation of quantum statistics to calculate both momentum- and coordinate-depending distributions and average values of quantum operators for many-fermion Coulomb systems. We discovered that the single-particle momentum distribution function deviates from the ideal Fermi distribution and forms the so-called “quantum tails” at high momenta, if non-ideality is strong enough in both degenerate and non-degenerate cases. This effect is always followed by the appearance of the short-range order on pair correlation functions and can be explained by the tunneling through the effective potential wells surrounding the electrons. Furthermore, we calculated the average kinetic and potential energies in the wide range of states, expanding our previous results significantly