12 research outputs found
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 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
Π Π΅Π΄ΠΊΠΈΠΉ ΡΠ»ΡΡΠ°ΠΉ Π²Π΅ΡΡ ΡΡΠ΅ΡΠ½ΠΎΠΉ ΡΠΎΡΠΌΡ Π³ΠΈΠΏΠ΅ΡΡΡΠΎΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΊΠ°ΡΠ΄ΠΈΠΎΠΌΠΈΠΎΠΏΠ°ΡΠΈΠΈ Ρ Π²Π½ΡΡΡΠΈΠΆΠ΅Π»ΡΠ΄ΠΎΡΠΊΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΡΡΡΠΊΡΠΈΠ΅ΠΉ Ρ ΡΠ΅Π±Π΅Π½ΠΊΠ°
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.ΠΠΈΠΏΠ΅ΡΡΡΠΎΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΊΠ°ΡΠ΄ΠΈΠΎΠΌΠΈΠΎΠΏΠ°ΡΠΈΡ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΠ΅ΡΡΡ ΠΏΠ΅ΡΠ²ΠΈΡΠ½ΠΎΠΉ Π³ΠΈΠΏΠ΅ΡΡΡΠΎΡΠΈΠ΅ΠΉ ΠΌΠΈΠΎΠΊΠ°ΡΠ΄Π° ΠΏΡΠΈ ΠΎΡΡΡΡΡΡΠ²ΠΈΠΈ Π΄ΡΡΠ³ΠΈΡ
ΠΏΡΠΈΡΠΈΠ½ ΡΡΠΎΠ³ΠΎ, Π² ΡΠ°ΡΡΠ½ΠΎΡΡΠΈ Π°ΡΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ Π³ΠΈΠΏΠ΅ΡΡΠ΅Π½Π·ΠΈΠΈ. ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ ΡΠ΅Π΄ΠΊΠΈΠΉ ΡΠ»ΡΡΠ°ΠΉ Π²Π΅ΡΡ
ΡΡΠ΅ΡΠ½ΠΎΠΉ Π³ΠΈΠΏΠ΅ΡΡΡΠΎΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΊΠ°ΡΠ΄ΠΈΠΎΠΌΠΈΠΎΠΏΠ°ΡΠΈΠΈ Ρ Π΄Π΅Π²ΠΎΡΠΊΠΈ 7 Π»Π΅Ρ Ρ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΡΠΌΠΈ Π½Π΅ΡΠΏΠ΅ΡΠΈΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΠΊΠ»ΠΈΠ½ΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΠΏΡΠΎΡΠ²Π»Π΅Π½ΠΈΡΠΌΠΈ (Π³ΠΎΠ»ΠΎΠ²Π½ΡΠ΅ Π±ΠΎΠ»ΠΈ, ΠΏΡΠΎΠ²ΠΎΡΠΈΡΡΠ΅ΠΌΡΠ΅ Π½Π°Π³ΡΡΠ·ΠΊΠ°ΠΌΠΈ). ΠΡΠΈ ΠΏΠ»Π°Π½ΠΎΠ²ΠΎΠΌ ΠΎΠ±ΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΈ Π±ΡΠ»ΠΈ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½Ρ ΡΠΈΠΏΠΈΡΠ½ΡΠ΅ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ Π½Π° ΠΠΠ - Π²ΡΡΠ°ΠΆΠ΅Π½Π½ΡΠ΅ Π½Π°ΡΡΡΠ΅Π½ΠΈΡ ΡΠ΅ΠΏΠΎΠ»ΡΡΠΈΠ·Π°ΡΠΈΠΈ ΠΌΠΈΠΎΠΊΠ°ΡΠ΄Π° ΠΈ Π³Π»ΡΠ±ΠΎΠΊΠΈΠ΅ (Π΄ΠΎ 10 ΠΌΠΌ) ΠΎΡΡΠΈΡΠ°ΡΠ΅Π»ΡΠ½ΡΠ΅ Π·ΡΠ±ΡΡ Π’ Π² Π³ΡΡΠ΄Π½ΡΡ
ΠΎΡΠ²Π΅Π΄Π΅Π½ΠΈΡΡ
. Π’ΡΠ°Π½ΡΡΠΎΡΠ°ΠΊΠ°Π»ΡΠ½Π°Ρ ΡΡ
ΠΎΠΊΠ°ΡΠ΄ΠΈΠΎΠ³ΡΠ°ΡΠΈΡ Π²ΡΡΠ²ΠΈΠ»Π° Π»ΠΎΠΊΠ°Π»ΡΠ½ΡΡ ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΡΠ½ΡΡ Π³ΠΈΠΏΠ΅ΡΡΡΠΎΡΠΈΡ Π²Π΅ΡΡ
ΡΡΠ΅ΡΠ½ΡΡ
ΠΎΡΠ΄Π΅Π»ΠΎΠ² Π»Π΅Π²ΠΎΠ³ΠΎ ΠΆΠ΅Π»ΡΠ΄ΠΎΡΠΊΠ° Ρ Π½Π°ΡΡΡΠ΅Π½ΠΈΠ΅ΠΌ ΠΈΡ
ΡΠΎΠΊΡΠ°ΡΠΈΠΌΠΎΡΡΠΈ ΠΈ Π²Π½ΡΡΡΠΈΠΆΠ΅Π»ΡΠ΄ΠΎΡΠΊΠΎΠ²ΡΡ ΠΎΠ±ΡΡΡΡΠΊΡΠΈΡ Ρ Π³ΡΠ°Π΄ΠΈΠ΅Π½ΡΠΎΠΌ Π΄Π°Π²Π»Π΅Π½ΠΈΡ ΠΌΠ΅ΠΆΠ΄Ρ Π²Π΅ΡΡ
ΡΡΠ΅ΡΠ½ΡΠΌ ΠΈ ΡΡΠ΅Π΄Π½ΠΈΠΌ ΠΎΡΠ΄Π΅Π»Π°ΠΌΠΈ 30 ΠΌΠΌ ΡΡ.ΡΡ., ΡΡΠΎ Π±ΡΠ»ΠΎ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠΆΠ΄Π΅Π½ΠΎ Π΄Π°Π½Π½ΡΠΌΠΈ Π²Π΅Π½ΡΡΠΈΠΊΡΠ»ΠΎΠ³ΡΠ°ΡΠΈΠΈ ΠΈ ΡΡΠΈΠ½ΡΠΈΠ³ΡΠ°ΡΠΈΠΈ ΠΌΠΈΠΎΠΊΠ°ΡΠ΄Π°. ΠΠ Π’ ΡΠ΅ΡΠ΄ΡΠ° ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΠ»Π° ΡΡΡΠ°Π½ΠΎΠ²ΠΈΡΡ Π½Π°Π»ΠΈΡΠΈΠ΅ Π²ΡΡΠ°ΠΆΠ΅Π½Π½ΠΎΠΉ ΡΠΈΠ±ΡΠΎΠ·Π½ΠΎΠΉ ΡΡΠ°Π½ΡΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π²Π΅ΡΡ
ΡΡΠΊΠΈ Π»Π΅Π²ΠΎΠ³ΠΎ ΠΆΠ΅Π»ΡΠ΄ΠΎΡΠΊΠ°. ΠΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΡΡ Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΡΠ»ΡΡΠ°Ρ ΡΠ²Π»ΡΡΡΡΡ Π΄Π΅ΡΡΠΊΠΈΠΉ Π²ΠΎΠ·ΡΠ°ΡΡ ΠΏΠ°ΡΠΈΠ΅Π½ΡΠΊΠΈ ΠΈ ΡΠΎΡΠ΅ΡΠ°Π½ΠΈΠ΅ Π²Π΅ΡΡ
ΡΡΠ΅ΡΠ½ΠΎΠΉ Π³ΠΈΠΏΠ΅ΡΡΡΠΎΡΠΈΠΈ ΠΌΠΈΠΎΠΊΠ°ΡΠ΄Π° Ρ Π²Π½ΡΡΡΠΈΠΆΠ΅Π»ΡΠ΄ΠΎΡΠΊΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΡΡΡΠΊΡΠΈΠ΅ΠΉ
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 β 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 singleβmomentum 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 βquantum tailsβ 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