scholarly journals ON THE STABILITY OF PERIODICALLY TIME-DEPENDENT QUANTUM SYSTEMS

2008 ◽  
Vol 20 (06) ◽  
pp. 725-764 ◽  
Author(s):  
P. DUCLOS ◽  
E. SOCCORSI ◽  
P. ŠŤOVÍČEK ◽  
M. VITTOT
Keyword(s):  
Transition Probabilities ◽  
Initial Conditions ◽  
Energy Levels ◽  
Sufficient Conditions ◽  
Energy Operator ◽  
Mean Value ◽  
Quantum Systems ◽  
Time Dependent ◽  
Dense Subspace ◽  
Periodically Driven

The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e. conditions under which it holds true sup t ∈ ℝ|〈ψt, H(t)ψt〉| < ∞ where ψt denotes a trajectory at time t of the quantum system under consideration. We start from an analysis of the domain of the quasi-energy operator. Next, we show, under certain assumptions, that if the spectrum of the monodromy (Floquet) operator U(T, 0) is pure point then there exists a dense subspace of initial conditions for which the mean value of the energy is uniformly bounded in the course of time. Further, we show that if the propagator admits a differentiable Floquet decomposition then ‖H(t)ψt‖ is bounded in time for any initial condition ψ0, and one employs the quantum KAM algorithm to prove the existence of this type of decomposition for a fairly large class of H(t). In addition, we derive bounds uniform in time on transition probabilities between different energy levels, and we also propose an extension of this approach to the case of a higher order of differentiability of the Floquet decomposition. The procedure is demonstrated on a solvable example of the periodically time-dependent harmonic oscillator.

On the interaction between a time-dependent field and a two-level atom

2019 ◽  
Vol 34 (10) ◽  
pp. 1950081 ◽  
Author(s):  
N. H. Abdel-Wahab ◽  
Ahmed Salah
Keyword(s):  
Quantum Electrodynamics ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Quantum Systems ◽  
Trapped Ions ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Level Atom ◽  
Dependent Field

In this paper, we study the interaction between the time-dependent field and a two-level atom with one mode electromagnetic field. We consider that the field of photons is assumed to be coupled with modulated coupling parameter which depends explicitly on time. It is shown that the considered model can be reduced to a well-known form of the time-dependent generalized Jaynes–Cummings model. Under special initial conditions, in which the atom and the field are prepared in the excited and the coherent states, respectively, the explicit time evolution of the wave function of the entire system is analytically obtained. Our proposal has many advantages over the previous optical schemes and can be realized in several multiple experiments, such as trapped ions and quantum electrodynamics cavity. The influence of the time-dependent field parameter on the collapses-revivals, the normal squeezing of the radiation, the anti-bunching of photons and the entanglement phenomena for the considered atomic system is examined. The linear entropy, the von Neumann entropy are used to quantify entanglement in the quantum systems. We noticed that these phenomena are affected by the existence of both the time-dependent coupling field and detuning parameters.

scholarly journals Continuous-time quantum search and time-dependent two-level quantum systems

2019 ◽  
Vol 17 (03) ◽  
pp. 1950025 ◽  
Author(s):  
Carlo Cafaro ◽  
Paul M. Alsing
Keyword(s):  
Continuous Time ◽  
Transition Probabilities ◽  
Search Algorithm ◽  
Quantum Systems ◽  
Time Dependent ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Time Quantum ◽  
Characteristic Features ◽  
External Time

It was recently emphasized by Byrnes, Forster and Tessler [Phys. Rev. Lett. 120 (2018) 060501] that the continuous-time formulation of Grover’s quantum search algorithm can be intuitively understood in terms of Rabi oscillations between the source and the target subspaces. In this work, motivated by this insightful remark and starting from the consideration of a time-independent generalized quantum search Hamiltonian as originally introduced by Bae and Kwon [Phys. Rev. A 66 (2002) 012314], we present a detailed investigation concerning the physical connection between quantum search Hamiltonians and exactly solvable time-dependent two-level quantum systems. Specifically, we compute in an exact analytical manner the transition probabilities from a source state to a target state in a number of physical scenarios specified by a spin-[Formula: see text] particle immersed in an external time-dependent magnetic field. In particular, we analyze both the periodic oscillatory as well as the monotonic temporal behaviors of such transition probabilities and, moreover, explore their analogy with characteristic features of Grover-like and fixed-point quantum search algorithms, respectively. Finally, we discuss from a physics standpoint the connection between the schedule of a search algorithm, in both adiabatic and nonadiabatic quantum mechanical evolutions, and the control fields in a time-dependent driving Hamiltonian.

scholarly journals Um recorte histórico das contribuições de Erwin Schrödinger para a Mecânica Quântica

2021 ◽  
Vol 7 (1) ◽  
pp. 42
Author(s):  
Rafaelle da Silva Souza
Keyword(s):  
Energy Levels ◽  
Academic Research ◽  
History Of Physics ◽  
Quantum Systems ◽  
Time Dependent ◽  
Historical Overview ◽  
Wave Mechanics ◽  
Great Scientist ◽  
Erwin Schrödinger ◽  
History Of

Erwin Schrödinger (1887-1961) foi um físico austríaco, um grande cientista que viveu em um contexto europeu de mudança e turbulência, mas isso não o impediu de ter uma vida muito intensa, tanto em sua pesquisa científica quanto em sua vida pessoal. Seu trabalho mais famoso, publicado em 1926, inclui sua teoria da mecânica ondulatória, no qual consta a famosa equação que tem hoje o seu nome. Ele mostrou que a equação funcionava adequadamente para calcular os níveis de energia do átomo de hidrogênio. Em outros trabalhos, publicados no mesmo período, mostrou outras aplicações designadas ao oscilador harmônico e uma generalização para o caso dependente do tempo. Sua dedicação aos sistemas quânticos lhe rendeu o Prêmio Nobel em 1933. É sobre esse homem fascinante e complexo que se apresenta um recorte histórico com potencial para atrair não apenas os cientistas, mas qualquer pessoa interessada na história de nossos tempos, na vida e no pensamento de um dos maiores cientistas do século XX. O presente artigo nasceu do fato de que, embora muito se fale sobre Schrödinger, não há textos em língua portuguesa que ultrapassem os limites biográficos, apesar de sua extrema relevância teórica para a pesquisa acadêmica. Nesse sentido, tem-se por objetivo visitar algumas obras que relatam os acontecimentos ou fatos econômicos, políticos, sociais e culturais que resultaram no período mais produtivo da carreira de Schrödinger.A historical overview of Erwin Schrödinger’s contributions to Quantum MechanicsAbstractErwin Schrödinger (1887-1961) was an Austrian physicist, a great scientist who lived in a European context of change and turmoil, but this did not stop him from living a very intense life, both in his scientific research and in his personal life. His most famous work, published in 1926, includes his theory of wave mechanics, which contains the famous equation that bears his name today. He showed that the equation worked properly for calculating the energy levels of the hydrogen atom. In other works, published in the same period, he showed other applications assigned to the harmonic oscillator and a generalization for the time dependent case. His dedication to quantum systems won him the Nobel Prize in 1933. It is about this fascinating and complex man who presents a historical snippet with the potential to attract not only scientists, but anyone interested in the history of our times, life and thought from one of the greatest scientists of the 20th century. This article was born from the fact that, although much is said about Schrödinger, there are no texts in Portuguese that go beyond biographical limits, despite its extreme theoretical relevance for academic research. In this sense, the objective is to visit some works that report the economic, political, social and cultural events or facts that resulted in the most productive period of Schrödinger's career.Keywords: Quantum mechanics; Schrödinger; History of Physics.

COLLECTIVE QUADRUPOLE EXCITATIONS WITHIN A SELF-CONSISTENT APPROACH

2006 ◽  
Vol 15 (02) ◽  
pp. 379-386 ◽  
Author(s):  
L. PRÓCHNIAK
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Low Energy ◽  
Time Dependent ◽  
Collective Excitations ◽  
Skyrme Interaction ◽  
Self Consistent ◽  
Consistent Approach

Low energy quadrupole collective excitations are investigated using a model based on the Adiabatic Time Dependent HFB theory. Distinctive feature of proposed method is an extension of the collective space by adding variables referring to pairing degrees of freedom. In the microscopic part of the model effective Skyrme interaction and constant G pairing force are employed. Calculated energy levels and B(E2) transition probabilities in the 128 Xe nucleus are compared with the experimental data.

scholarly journals New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV)

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 48
Author(s):  
M. Raineri ◽  
M. Gallardo ◽  
J. Reyna Almandos ◽  
A. G. Trigueiros ◽  
C. J. B. Pagan
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Pulsed Discharge ◽  
Core Polarization ◽  
Polarization Effects ◽  
Hartree Fock ◽  
Theta Pinch ◽  
New Energy ◽  
First Time

A capillary pulsed-discharge and a theta-pinch were used to record Kr spectra in the region of 330–4800 Å. A set of 168 transitions of these spectra were classified for the first time. We extended the analysis to twenty-five new energy levels belonging to 3s23p24d, 3s23p25d even configurations. We calculated weighted transition probabilities (gA) for all of the experimentally observed lines and lifetimes for new energy levels using a relativistic Hartree–Fock method, including core-polarization effects.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals Sufficient conditions for adiabaticity in open quantum systems

2020 ◽  
Vol 102 (5) ◽  
Author(s):  
Alan C. Santos ◽  
Marcelo S. Sarandy
Keyword(s):  
Open Quantum Systems ◽  
Sufficient Conditions ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Time Dependent Lyotropic Chromonic Textures in Microfluidic Confinements

Crystals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 35 ◽  
Author(s):  
Anshul Sharma ◽  
Irvine Lian Hao Ong ◽  
Anupam Sengupta
Keyword(s):  
Phase Transition ◽  
Aspect Ratio ◽  
Temporal Dynamics ◽  
Initial Conditions ◽  
Flow Behavior ◽  
Medical Diagnostics ◽  
Time Dependent ◽  
Disodium Cromoglycate ◽  
M Phase ◽  
Static Conditions

Nematic and columnar phases of lyotropic chromonic liquid crystals (LCLCs) have been long studied for their fundamental and applied prospects in material science and medical diagnostics. LCLC phases represent different self-assembled states of disc-shaped molecules, held together by noncovalent interactions that lead to highly sensitive concentration and temperature dependent properties. Yet, microscale insights into confined LCLCs, specifically in the context of confinement geometry and surface properties, are lacking. Here, we report the emergence of time dependent textures in static disodium cromoglycate (DSCG) solutions, confined in PDMS-based microfluidic devices. We use a combination of soft lithography, surface characterization, and polarized optical imaging to generate and analyze the confinement-induced LCLC textures and demonstrate that over time, herringbone and spherulite textures emerge due to spontaneous nematic (N) to columnar M-phase transition, propagating from the LCLC-PDMS interface into the LCLC bulk. By varying the confinement geometry, anchoring conditions, and the initial DSCG concentration, we can systematically tune the temporal dynamics of the N- to M-phase transition and textural behavior of the confined LCLC. Overall, the time taken to change from nematic to the characteristic M-phase textures decreased as the confinement aspect ratio (width/depth) increased. For a given aspect ratio, the transition to the M-phase was generally faster in degenerate planar confinements, relative to the transition in homeotropic confinements. Since the static molecular states register the initial conditions for LC flows, the time dependent textures reported here suggest that the surface and confinement effects—even under static conditions—could be central in understanding the flow behavior of LCLCs and the associated transport properties of this versatile material.

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