Search results for "Nonlinear"
showing 10 items of 3684 documents
SCALING THEORY AND THE CLASSIFICATION OF PHASE TRANSITIONS
1992
The recent classification theory for phase transitions (R. Hilfer, Physica Scripta 44, 321 (1991)) and its relation with the foundations of statistical physics is reviewed. First it is outlined how Ehrenfests classification scheme can be generalized into a general thermodynamic classification theory for phase transitions. The classification theory implies scaling and multiscaling thereby eliminating the need to postulate the scaling hypothesis as a fourth law of thermodynamics. The new classification has also led to the discovery and distinction of nonequilibrium transitions within equilibrium statistical physics. Nonequilibrium phase transitions are distinguished from equilibrium transiti…
Instability of single-frequency operation in semilinear photorefractive coherent oscillators.
2002
The transition of the single-frequency oscillation of a semilinear photorefractive coherent oscillator for sufficiently large coupling strengths into two-frequency oscillation is predicted and is observed experimentally. The critical value of the coupling strength at which the bifurcation occurs is a function of pump intensity ratio and cavity losses. The supercritical bifurcation in the oscillation spectrum is analogous to the second-order phase transition.
Second-order optical phase transition in a semilinear photorefractive oscillator with two counterpropagating pump waves
2002
Soft-mode onset of coherent oscillation is revealed in a semilinear cavity with two counterpropagating pump waves. From the dynamics of the oscillation intensity and the dynamics of the grating decay with the feedback applied, critical behavior is detected: Both the characteristic time of oscillation onset and grating decay time go to infinity exactly at the threshold coupling strength. A conclusion is made about the similarity of this type of oscillator to the second-order phase transition.
Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
2015
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with …
Discreteness effects on a sine-Gordon breather
1991
We employ collective-variable theory to describe the dynamics of a breather excitation in its center-of-mass frame in continuous and discrete systems of one spatial dimension. The exact equations of motion for the collective variable and coupled phonon field are derived for any system which supports breatherlike excitations that have even spatial parity where the collective variable represents half the distance between the breather subkinks. We then specialize the theory to the sine-Gordon (SG) case. For the continuum SG system we derive the exact effective potential in terms of the collective variable and discuss the relativistic effects on the breather subkinks which are quite different t…
Optomechanical systems close to the conservative limit
2017
In dissipative optomechanical systems, the total damping hits negative values at the parametric instability point. This also corresponds to the phonon lasing threshold, where the mechanical resonator enters in the self-induced oscillations regime. This paper shows that the two mentioned phenomena are delayed from each other when the optomechanical systems operate close to their conservative limit, where the mechanical damping is very small. In fact, the total damping can be negative and very small for a while before the phonon lasing happens. As a result, the linearized theory is extended over the negative damping region where the mechanical displacements remain very small. It follows that …
Some physical appearances of vector coherent states and coherent states related to degenerate Hamiltonians
2005
In the spirit of some earlier work on the construction of vector coherent states over matrix domains, we compute here such states associated to some physical Hamiltonians. In particular, we construct vector coherent states of the Gazeau-Klauder type. As a related problem, we also suggest a way to handle degeneracies in the Hamiltonian for building coherent states. Specific physical Hamiltonians studied include a single photon mode interacting with a pair of fermions, a Hamiltonian involving a single boson and a single fermion, a charged particle in a three dimensional harmonic force field and the case of a two-dimensional electron placed in a constant magnetic field, orthogonal to the plane…
Strong-field high-frequency approximation to the multiphoton ionization of hydrogen
1990
The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.
Photoelectric effect from a metal surface: a revisited theoretical model
1992
The Sommerfeld model extended to include radiation–electron interaction in the regime of highly intense fields is taken as the basis for studying theoretically the laser multiphoton photoelectric effect from a metal surface. Numerical analysis is carried out without approximations other than those inherent in the model itself; the study of the multiphoton aspect of the problem is based on a scheme that is nonperturbative in an essential way. The numerical analysis facilitates insight into the potential and the limits of the model in the interpretation of recent experiments and into the similarities and differences between the metal multiphoton effect and atomic multiphoton ionization. The r…
Ray-tracing through N-body simulations and CMB anisotropy estimations
2007
The fully nonlinear evolution of galaxy clusters and substructures –given by N-body simulations– is used to simulate maps of the Rees-Sciama (RS) effect. The universe is covered by simulation boxes and photons move across them. A recent technique for ray-tracing through N-body simulations is described in detail and implemented. It is based on the existence of preferred directions (to move photons through the boxes), and also on the use of an appropriate cutoff. By the moment, only small RS maps (around 2×2) have been obtained with this technique. We justify that our ray-tracing procedure is also appropriate in the case of large simulation cubes (∼ 1000 Mpc per edge), where high enough resol…