Band 71, Heft 10 - Focus Section: Emergence in Driven Solid-State and Cold-Atom Systems / Guest Editors: Ludwig Mathey, Junichi Okamoto

We suggest to subject anharmonically trapped Bose–Einstein condensates to sinusoidal forcing with a smooth, slowly changing envelope, and to measure the coherence of the system after such pulses. In a series of measurements with successively increased maximum forcing strength, one then expects an adiabatic return of the condensate to its initial state as long as the pulses remain sufficiently weak. In contrast, once the maximum driving amplitude exceeds a certain critical value there should be a drastic loss of coherence, reflecting significant heating induced by the pulse. This predicted experimental signature is traced to the loss of an effective adiabatic invariant, and to the ensuing breakdown of adiabatic motion of the system’s Floquet state when the many-body dynamics become chaotic. Our scenario is illustrated with the help of a two-site model of a forced bosonic Josephson junction, but should also hold for other, experimentally accessible configurations.

The topological properties of periodically driven many-body systems often have no static analogs and defy a simple description based on the effective Hamiltonian. To explore the emergent edge modes in driven p -wave superconductors in two dimensions, we analysed a toy model of Kitaev chains (one-dimensional spinless p -wave superconductors with Majorana edge states) coupled by time-periodic hopping. We showed that with proper driving, the coupled Kitaev chains can turn into a fully gapped superconductor, which is analogous to the p x + ip y state but has two, rather than one, chiral edge modes. A different driving protocol turns it into a gapless superconductor with isolated point nodes and completely flat edge states at quasienergy ω =0 or π / T , with T as the driving period. The time evolution operator U ( k x , k y , t ) of the toy model is computed exactly to yield the phase bands. And the “topological singularities” of the phase bands are exhausted and compared to those of a periodically driven Hofstadter model, which features counter-propagating chiral edge modes. These examples demonstrate the unique edge states in driven superconducting systems and suggest driving as a potentially fruitful route to engineer new topological superconductors.

Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasi-periodically driven quantum systems can be treated with generalisations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalisation of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.

We investigate multi-“photon” interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.

We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and in the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving term with a cosine dependence on time, up to fourth order. We apply these to the steady state of a classical parametric oscillator coupled to a thermal bath, which we solve numerically for comparison. Beyond dynamical stabilisation at second order, we find that the higher orders further renormalise the oscillator frequency, and additionally create a weakly renormalised effective temperature. The renormalised oscillator frequency is quantitatively accurate almost up to the parametric instability, as we confirm numerically. Additionally, a cut-off dependent term is generated, which indicates the break down of the hierarchy of time scales of the system, as a precursor to the instability. Finally, we apply this formalism to a parametrically driven chain, as an example for the control of the dispersion of a many-body system.

The pseudo-differential operators are used to construct the non-auto Darboux transformation (DT) for extended C-type of KP (CKP) hierarchy and the corresponding generalised Wronskian solutions are derived. In addition, explicit solutions of soliton-type are formulated for the second type of CKP equation with self-consistent sources (CKPESCS).

In this article, a transverse dynamic deflection model is established for thin plate made of saturated porous materials. Based on the Biot’s model for fluid-saturated porous media, using the Love–Kirchhoff hypothesis, the governing equations of transverse vibrations of fluid-saturated poroelastic plates are derived in detail, which take the inertial, fluid viscous, mechanical couplings, compressibility of solid, and fluid into account. The free vibration and forced vibration response of a simply supported poroelastic rectangular plate is obtained by Fourier series expansion method. Through numerical examples, the effect of porosity and permeability on the dynamic response, including the natural frequency, amplitude response, and the resonance areas is assessed.

The present paper reports a study on accreting tachyon, Dirac-Born-Infeld essence and h-essence scalar field models of dark energy onto Morris-Thorne wormhole. Using three different parameterisation schemes and taking H = H0 + H1t$H\, = \,{H_0}\, + \,{{{H_1}} \over t}$, we have derived the mass of the wormhole for all of the three parameterisation schemes that are able to get hold of both quintessence and phantom behaviour. With suitable choice of parameters, we observed that accreting scalar field dark energy models are increasing the mass of the wormhole in the phantom phase and the mass is decreasing in the quintessence phase. Finally, we have considered accretion with power law form of scale factor and without any parameterisation scheme for the equation of state parameter and observed the fact that phantom-type dark energy supports the existence of wormholes.

Based on the modified Darboux transformation method, starting from zero solution and the plane wave solution, the hierarchies of rational solutions and breather solutions with “high frequency” and “low frequency” of the coupled nonlinear Schrödinger equation in parity-time symmetric nonlinear couplers with gain and loss are constructed, respectively. From these results, some basic characteristics of multi-rogue waves and multi-breathers are studied. Based on the property of rogue wave as the “quantum” of pattern structure in rogue wave hierarchy, we further study the novel structures of the superposed Akhmediev breathers, Kuznetsov-Ma solitons and their combined structures. It is expected that these results may give new insight into the context of the optical communications and Bose-Einstein condensations.

The multimode characteristics of the space-charge wave are investigated in a cylindrical waveguide complex plasma. The dispersion relation of the space-charge wave is derived in a waveguide, including two-temperature electrons. The results show that the wave frequencies in a plasma with a high population of high-temperature electrons are always smaller those in a plasma with a low population of high-temperature electrons. It is also found that the population of high-temperature electrons suppresses the group velocity of the space-charge wave. In addition, it is found that the frequency increases with an increase in the radius of the cylindrical wave guide. The variations of the frequency and the group velocity due to the density, temperature, and geometric effects are also discussed.