Reciprocity of thermal diffusion in time-modulated systems

The reciprocity principle governs the symmetry in transmission of electromagnetic and acoustic waves, as well as the diffusion of heat between two points in space, with important consequences for thermal management and energy harvesting. There has been significant recent interest in materials with time-modulated properties, which have been shown to efficiently break reciprocity for light, sound, and even charge diffusion. However, time modulation may not be a plausible approach to break thermal reciprocity, in contrast to the usual perception. We establish a theoretical framework to accurately describe the behavior of diffusive processes under time modulation, and prove that thermal reciprocity in dynamic materials is generally preserved by the continuity equation, unless some external bias or special material is considered. We then experimentally demonstrate reciprocal heat transfer in a time-modulated device. Our findings correct previous misconceptions regarding reciprocity breaking for thermal diffusion, revealing the generality of symmetry constraints in heat transfer, and clarifying its differences from other transport processes in what concerns the principles of reciprocity and microscopic reversibility.

Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice

We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information.

Global analysis of crystal energy landscapes: applying the threshold algorithm to molecular crystal structures

We describe the implementation of the Monte Carlo threshold algorithm for molecular crystals as a method to provide an estimate of the energy barriers separating crystal structures. By sampling the local energy minima accessible from multiple starting structures, the simulations yield a global picture of the crystal energy landscapes. This provides valuable information on the depth of the energy minima associated with crystal structures and adds to the information available from crystal structure prediction methods that are used for anticipating polymorphism. We present results from applying the threshold algorithm to four polymorphic organic molecular crystals, examine the influence of applying space group symmetry constraints during the simulations, and discuss the relationship between the structure of the energy landscape and the intermolecular interactions present in the crystals.

Onset of absolutely unstable behaviour in the Stokes layer: a Floquet approach to the Briggs method

For steady flows, the Briggs (Electron-Stream Interaction with Plasmas. MIT Press, 1964) method is a well-established approach for classifying disturbances as either convectively or absolutely unstable. Here, the framework of the Briggs method is adapted to temporally periodic flows, with Floquet theory utilised to account for the time periodicity of the Stokes layer. As a consequence of the antiperiodicity of the flow, symmetry constraints are established that are used to describe the pointwise evolution of the disturbance, with the behaviour governed by harmonic and subharmonics modes. On coupling the symmetry constraints with a cusp-map analysis, multiple harmonic and subharmonic cusps are found for each Reynolds number of the flow. Therefore, linear disturbances experience subharmonic growth about fixed spatial locations. Moreover, the growth rate associated with the pointwise development of the disturbance matches the growth rate of the disturbance maximum. Thus, the onset of the Floquet instability (Blennerhassett & Bassom, J. Fluid Mech., vol. 464, 2002, pp. 393–410) coincides with the onset of absolutely unstable behaviour. Stability characteristics are consistent with the spatio-temporal disturbance development of the family-tree structure that has hitherto only been observed numerically via simulations of the linearised Navier–Stokes equations (Thomas et al., J. Fluid Mech., vol. 752, 2014, pp. 543–571; Ramage et al., Phys. Rev. Fluids, vol. 5, 2020, 103901).

Cryo-EM single-particle structure refinement and map calculation using Servalcat

In 2020, cryo-EM single-particle analysis achieved true atomic resolution thanks to technological developments in hardware and software. The number of high-resolution reconstructions continues to grow, increasing the importance of the accurate determination of atomic coordinates. Here, a new Python package and program called Servalcat is presented that is designed to facilitate atomic model refinement. Servalcat implements a refinement pipeline using the program REFMAC5 from the CCP4 package. After the refinement, Servalcat calculates a weighted F o − F c difference map, which is derived from Bayesian statistics. This map helps manual and automatic model building in real space, as is common practice in crystallography. The F o − F c map helps in the visualization of weak features including hydrogen densities. Although hydrogen densities are weak, they are stronger than in the electron-density maps produced by X-ray crystallography, and some H atoms are even visible at ∼1.8 Å resolution. Servalcat also facilitates atomic model refinement under symmetry constraints. If point-group symmetry has been applied to the map during reconstruction, the asymmetric unit model is refined with the appropriate symmetry constraints.

Ratchet effect in brownian photomotors: symmetry constraints and going beyond them

The symmetry conditions have been derived for the occurrence of the ratchet effect in Brownian photomotors. To this end, spatiotemporal symmetry operations in vector transformations, coordinate and time shifts, and in the overdamped regime were applied to the average photomotor velocity taken as a functional of the coordinate- and time-dependent potential energy. As established, individual Brownian particles (molecules) can move directionally only provided a symmetrically distributed charge fluctuates in them and they are placed on the substrates with an antisymmetric charge distribution or, vice versa, they are characterized by antisymmetrically distributed charge fluctuations and are placed on symmetric substrates. The collective directed motion of orientation-averaged particles is possible only in the former case. If a particle charge distribution is described by a time dependence with the universal type of symmetry (i.e., simultaneously symmetric, antisymmetric, and shift-symmetric), an additional symmetry constraint on the ratchet functioning arises: the ratchet effect is ruled out in the overdamped regime but allowed for inertial moving particles if the charge distributions in both the particle and the substrate are neither symmetric nor antisymmetric. The effect of the universal type of symmetry is exemplified by dipole photomotors derived from donor-acceptor conjugated organic molecules. With a specific type of molecular photoexcitation and a specific relationship of the dipole moments in the ground and excited states, the ratchet effect becomes symmetry-forbidden. The forbiddenness can be removed by molecular polarization effects, which in this case become the predominant factor governing the direction of the motion and average velocity of photomotors. The estimated velocities of polarization photomotors are an order of magnitude larger than for known motor proteins and dipole Brownian photomotors. These results can be helpful in the purposeful molecular design of dipole photomotors.

Experimental realization of phase-controlled dynamics with hybrid digital–analog approach

Quantum simulation can be implemented in pure digital or analog ways, each with their pros and cons. By taking advantage of the universality of a digital route and the efficiency of analog simulation, hybrid digital–analog approaches can enrich the possibilities for quantum simulation. We use a hybrid approach to experimentally perform a quantum simulation of phase-controlled dynamics resulting from a closed-contour interaction (CCI) within certain multi-level systems in superconducting quantum circuits. Due to symmetry constraints, such systems cannot host an inherent CCI. Nevertheless, by assembling analog modules corresponding to their natural evolutions and specially designed digital modules constructed from standard quantum logic gates, we can bypass such constraints and realize an effective CCI in these systems. Based on this realization, we demonstrate a variety of related and interesting phenomena, including phase-controlled chiral dynamics, separation of chiral enantiomers, and a mechanism to generate entangled states based on CCI.

The reduction of the q-Wronskian solutions of the q-deformed modified KP hierarchy to its constrained case

By using the eigenfunction symmetry constraints of the [Formula: see text]-deformed modified Kadomtsev–Petviashvili ([Formula: see text]-mKP) hierarchy, we show a necessary and sufficient condition to reduce [Formula: see text]-Wronskian solutions of the [Formula: see text]-mKP hierarchy to the [Formula: see text]-cmKP ([Formula: see text]-deformed constrained modified Kadomtsev–Petviashvili) hierarchy defined by setting the Lax operator as [Formula: see text]. Then an illustrative example is given.