Search results for "Time evolution"
showing 10 items of 155 documents
Experimental evidence for fractional time evolution in glass forming materials
2002
The infinitesimal generator of time evolution in the standard equation for exponential (Debye) relaxation is replaced with the infinitesimal generator of composite fractional translations. Composite fractional translations are defined as a combination of translation and the fractional time evolution introduced in [Physica A, 221 (1995) 89]. The fractional differential equation for composite fractional relaxation is solved. The resulting dynamical susceptibility is used to fit broad band dielectric spectroscopy data of glycerol. The composite fractional susceptibility function can exhibit an asymmetric relaxation peak and an excess wing at high frequencies in the imaginary part. Nevertheless…
Uniform analytic description of dephasing effects in two-state transitions
2007
We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, …
Quantum signatures in the dynamics of two dipole-dipole interacting soft dimers
2006
The quantum covariances of physically transparent pairs of observables relative to two dimers hosted in a solid matrix are exactly investigated in the temporal domain. Both dimers possess fermionic and bosonic degrees of freedom and are dipolarly coupled. We find out and describe clear signatures traceable back to the presence and persistence of quantum coherence in the time evolution of the system. Manifestations of a competition between intramolecular and intermolecular energy migration mechanisms are brought to light. The experimental relevance of our results is briefly commented.
Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices
2013
The difference between boson and fermion dynamics in quasi-one-dimensional lattices is studied by calculating the persistent current in small quantum rings and by exact simulations of the time evolution of the many-particle state in two cases: expansion of a localized cloud and collisions in a Newton’s cradle. We consider three different lattices which in the tight-binding model exhibit flat bands. The physical realization is considered to be an optical lattice with bosonic or fermionic atoms. The atoms are assumed to interact with a repulsive short-range interaction. The different statistics of bosons and fermions lead to different dynamics. Spinless fermions are easily trapped in the flat…
Quantum many-body dynamics of coupled double-well superlattices
2008
We propose a method for controllable generation of non-local entangled pairs using spinor atoms loaded in an optical superlattice. Our scheme iteratively increases the distance between entangled atoms by controlling the coupling between the double wells. When implemented in a finite linear chain of 2N atoms, it creates a triplet valence bond state with large persistency of entanglement (of the order of N). We also study the non-equilibrium dynamics of the one-dimensional ferromagnetic Heisenberg Hamiltonian and show that the time evolution of a state of decoupled triplets on each double well leads to the formation of a highly entangled state where short-distance antiferromagnetic correlatio…
Collective behavior ofMbosonic modes interacting with a single two-level atom
1988
The Hamiltonian describing, without the rotating-wave approximation (RWA), the linear interaction between M bosonic modes with an Einstein spectrum and a single two-level atom is exactly and canonically transformed introducing M suitable collective independent field modes, in such a way that only one among them is coupled to the atom. Some physical consequences of this fact are analyzed and, in particular, the existence of radiation-trapping phenomena together with the possibility of atomic absorption suppression is established. The applicability of the RWA to this system is discussed and the importance of the effective-field statistics for the time evolution of the system is pointed out.
Spinodal decomposition of polymer solutions: molecular dynamics simulations of the two-dimensional case.
2012
As a generic model system for phase separation in polymer solutions, a coarse-grained model for hexadecane/carbon dioxide mixtures has been studied in two-dimensional geometry. Both the phase diagram in equilibrium (obtained from a finite size scaling analysis of Monte Carlo data) and the kinetics of state changes caused by pressure jumps (studied by large scale molecular dynamics simulations) are presented. The results are compared to previous work where the same model was studied in three-dimensional geometry and under confinement in slit geometry. For deep quenches the characteristic length scale ℓ(t) of the formed domains grows with time t according to a power law close to [Formula: see…
Adaptive mesh reconstruction for hyperbolic conservation laws with total variation bound
2012
We consider 3-point numerical schemes, that resolve scalar conservation laws, that are oscillatory either to their dispersive or anti-diffusive nature. The spatial discretization is performed over non-uniform adaptively redefined meshes. We provide a model for studying the evolution of the extremes of the oscillations. We prove that proper mesh reconstruction is able to control the oscillations; we provide bounds for the Total Variation (TV) of the numerical solution. We, moreover, prove under more strict assumptions that the increase of the TV, due to the oscillatory behavior of the numerical schemes, decreases with time; hence proving that the overall scheme is TV Increase-Decreasing (TVI…
Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness
2020
Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of the springpot is defined in terms of a single integral with separable kernel endowed with a non-linear transform of the state variable that allows for the use of Boltzmann superposition. The model represents a self-similar hierarchy that allows for a time-invariance as the result of the application of the conservation laws at any resolution scale. It is shown that the non-linear spring…
Tracking the time-evolution of the electron distribution function in Copper by femtosecond broadband optical spectroscopy
2019
Multitemperature models are nowadays often used to quantify the ultrafast electron-phonon (boson) relaxations and coupling strengths in advanced quantum solids. To test their applicability and limitations, we perform systematic studies of carrier relaxation dynamics in copper, a prototype system for which the two-temperature model (TTM) was initially considered. Using broadband time-resolved optical spectroscopy, we study the time evolution of the electron distribution function, $f(E)$, over a large range of excitation densities. Following intraband optical excitation, $f(E)$ is found to be athermal over several 100 fs, with a substantial part of the absorbed energy already being transferre…