Spatially localized trains of soliton in attractive Bose-Einstein condensates with periodic potential

In solid state physics, it is an unsaid (tacit) assumption that the Bloch theorem is applicable to a crystal lattice even if it is of the macroscopic dimensions, provided periodicity is maintained. However, in a realistic situation, electrons in a periodic potential of ions constitute an open quantum system and are subjected to decoherence and dissipation. A natural question arises: up to what distances electrons in a periodic potential can be considered as constituting an effective closed quantum system? And what is the cause of decoherence? To answer some of these questions, the seminal theory of Ovchinnikov and Erikhman of decoherence due to ionic motion is revisited and an oversight of the authors is corrected. Correct conditions for decoherence to occur are worked out. Length scale up to which the motion of ions remains coherent is also calculated. Finally, a realistic physical picture is discussed.

Context: Quantum mechanical proton tunneling is a recognized but often phenomenologically treated factor in enzymatic catalysis and transport. Its explicit role as a governing principle in drug-protein binding and pH-triggered release kinetics remains poorly understood, lacking a predictive theoretical framework that connects nanoscale cavity geometry to functional pharmacological outcomes. Method: We developed an analytical model for proton confinement in drug-protein cavities by solving the one-dimensional time-independent Schrödinger equation, reduced from a Nuclear Time Dependent Schrödinger equation for two fundamental potential classes viz an asymmetric double-well potentials representing localized enzymatic transfer and periodic Kronig-Penney potentials for delocalized conduction along proton wires. Analytical eigenproblems yield low-lying states and tunneling splittings, cross-checked by instanton/WKB estimates; KP/TB bands and a WKB bridge provide an effective hopping . Within the parameter ranges explored, our computations indicate that sub-ångström changes in donor–acceptor distance can modify tunneling probabilities and KIEs by factors on the order of ∼5−20, and produce apparent pKₐ shifts on the order of ∼0.3−0.5 units, leading to roughly one–to–two-order changes in and associated half-lives. In the extended sector, diagonal energetic disorder reduces localization length in a manner consistent with Anderson-type localization, and a modeled pH step on a proton wire can bias a confined cavity on ps–ns timescales, contingent on the adopted couplings. These results are model-based and meant to provide design implications not absolute predictions highlighting how cavity geometry and hydrogen-bond network order may be tuned to modulate tunneling-assisted kinetics.

Abstract Nowadays a bit is no longer a mere abstraction but a physical quantity whose manipulation governs both operation of modern technologies and theoretical frontiers of fundamental science. In this work we propose a setup in which the memory time can be utilized to control the generation and storage of binary information. In particular, we consider a nonequilibrium Brownian particle immersed in a viscoelastic environment and dwelling in a spatially periodic potential. We interpret its average velocity as a bit and show that depending on the memory time characterizing the viscoelastic bath the particle can be either in one of two stable states representing the bit values or in a chaotic state in which the information is erased and a new bit can be generated. We analyze randomness of the so obtained bit sequence and assess the stability of the produced values. Our study provides a blueprint for storing and processing information in a microscopic system using its memory.

KAM tori for a nonlinear beam equation with an almost periodic potential based on the space variable

Accurate free-energy estimation is essential in molecular simulation, yet the periodic boundary conditions (PBC) commonly used in computer simulations have rarely been explicitly exploited. Equilibrium methods such as umbrella sampling, metadynamics, and adaptive biasing force require extensive sampling, while nonequilibrium pulling with Jarzynski's equality suffers from poor convergence due to exponential averaging. Here, we introduce a physics-informed, score-based diffusion framework: by mapping PBC simulations onto a Brownian particle in a periodic potential, we derive the Fokker-Planck steady-state score that directly encodes free-energy gradients. A neural network is trained on nonequilibrium trajectories to learn this score, providing a principled scheme to efficiently reconstruct the potential of mean force. On benchmark periodic potentials and small-molecule membrane permeation, our method is up to 1 order of magnitude more efficient than umbrella sampling.

We propose a superconducting qubit based on engineering the first and second harmonics of the Josephson energy and phase relation E J 1 cos  φ and E J 2 cos  2 φ . By constructing a circuit such that E J 2 is negative and | E J 1 | ≪ | E J 2 | , we create a periodic potential with two nondegenerate minima. The qubit, which we dub “harmonium,” is formed from the lowest-energy states of each minimum. Bit-flip protection of the qubit arises due to the localization of each qubit state to their respective minima, while phase-flip protection can be understood by considering the circuit within the Born-Oppenheimer approximation. We demonstrate with time-domain simulations that single- and two-qubit gates can be performed in approximately 100 ns. Finally, we compute the qubit coherence times using numerical diagonalization of the complete circuit in conjunction with state-of-the-art noise models. We estimate out-of-manifold heating times on the order of milliseconds, which can be treated as erasure errors using conventional dispersive readout. We estimate pure-dephasing times on the order of many tens of milliseconds, and bit-flip times on the order of seconds.

Abstract Thouless pumping, originally conceptualized as the quantized transport of electrons in a periodic potential, has recently received significant attention in topological photonics. The displacement of the wave in Thouless pumping is governed by the topological invariant known as the Chern number, which emerges from the adiabatic evolution of the potential. In photonic systems, the principles of Thouless pumping enable topologically protected light transport, thereby stimulating growing interest in photonics research. In recent years, numerous novel variants of optical Thouless pumping have emerged that extend beyond the conventional theoretical framework. Notable examples include nonlinear Thouless pumping, non‐Hermitian Thouless pumping, nonAbelian Thouless pumping, and quasi‐periodic Thouless pumping. Moreover, implementations of Thouless pumping are demonstrated across various innovative photonic platforms. This review systematically examines contemporary advancements in optical Thouless pumping, encompassing theoretical underpinnings and experimental implementations.

Engineering topological exciton structures in two-dimensional semiconductors by a periodic electrostatic potential

A highly periodic electrostatic potential and coherent band transport can emerge in organic molecular crystals, despite weak van der Waals interactions. Although charge carrier mobility in single-crystalline organic semiconductors (OSCs) reaches 10 square centimeters per volt per second (cm2V-1s-1), it is predominantly limited by molecular vibrations excited at room temperature. The extent to which mobility in single-crystalline OSCs can be increased remains a central question. Here, we demonstrate charge transport in a clean two-dimensional hole gas (2DHG) in uniaxially strained, single-crystalline OSCs at cryogenic temperatures, with minimized lattice vibrations. Hall effect measurements reveal a mobility of 117 cm2V-1s-1 at 2 kelvin under 2.8% compressional strain, with an extraordinarily large piezoresistive effect and low sheet resistivity of 550 ohms, one-fifth of the lowest resistivity in unstrained samples. These clean systems offer opportunities to explore intrinsic strain-induced charge transport physics, where condensed matter phenomena, characterized by weakly bonded molecular orbitals, combine electronic correlation and lattice degrees of freedom.

We investigate a Brownian heat engine wherein a particle moves through a periodic ratchet potential under an exponentially decreasing temperature profile, a spatial configuration that closely resembles experimentally realizable conditions such as laser-induced thermal gradients and thermoplasmonic heating. This model yields exact analytical expressions for the particle current, thermodynamic efficiency, entropy production, and coefficient of performance (COP), and uniquely recovers the Curzon-Ahlborn efficiency and the corresponding endoreversible COP exactly in the quasistatic limit. These findings provide a rare and rigorous realization of endoreversible thermodynamics at the mesoscopic scale because they are derived directly from microscopic stochastic dynamics without recourse to phenomenological assumptions, asymptotic approximations, or coarse-graining techniques. Although the derived efficiency and COP are exact, they remain strictly below the Carnot limit, reflecting the inherent irreversibility embedded within the endoreversible framework. Furthermore, we show that in comparison to linear and piecewise-constant temperature profile cases, the exponential temperature profile leads to significantly higher particle velocities and higher entropy production, but lower thermodynamic efficiency, which underscores the fundamental trade-off between transport speed and energy cost. We further extend our analysis to networks of interacting Brownian motors operating in spatially nonuniform thermal environments. Numerical simulations confirm our analytical predictions and reveal the critical roles of temporal dynamics and external load in shaping motor performance, as well as transport directionality. Importantly, the exponential temperature profile is not only analytically tractable but also experimentally viable, providing a powerful platform for probing the emergence of macroscopic thermodynamic behavior from the underlying microscopic nonequilibrium dynamics.

In this paper, we will study the following nonlinear elliptic equation with zero mass on the lattice graph \begin{equation}\label{A}\tag{A} \begin{cases} -\Delta_{p} u= K(x)f(u) & \hbox{in } \mathbb{Z}^N, \\ u\in D^{1, p}\big(\mathbb{Z}^N\big), \end{cases} \end{equation} where $ N\geq 3$, $1< p< N$, $K$ is a nonnegative potential function, $f$ is a continuous function with quasicritical growth or supercritical growth. By employing variational methods, we establish the existence of ground states for the above equation with an asymptotically periodic potential and vanishing potential at infinity. For the case of asymptotically periodic potential, we also generalize the main result from $\mathbb{Z}^N$ to quasi-transitive graphs.

We investigate diffusion in a two-dimensional inverted soft Lorentz gas, where attractive Fermi-type potential wells are arranged in a triangular lattice. This configuration contrasts with earlier studies of soft Lorentz gases involving repulsive scatterers. By systematically varying the gap width and softness of the potential, we explore a rich landscape of diffusive behaviors. We present numerical simulations of the mean-squared displacement and compute diffusion coefficients, identifying tonguelike structures in parameter space associated with quasiballistic transport. Furthermore, we develop an extension to the Machta-Zwanzig approximation that incorporates correlated multihop trajectories, and we correct for the influence of localized periodic orbits. Our findings highlight the qualitative and quantitative differences between inverted and repulsive soft Lorentz gases, and they offer new insights into transport phenomena in smooth periodic potentials.

Quantum droplets—arising from the delicate balance between repulsive and attractive interactions—continue to be of significant interest in the study of ultracold atomic systems. In this work, we revisit the ground-state properties and collective dynamics of one-dimensional quantum droplets. We identify a critical effective particle number, N=N_csim 8.5, at which the superfluid fraction f_s exhibits a distinct inflection point, indicating a structural transition in the ground state. For N<N_c, the density profile is sharply peaked, whereas for N>N_c, it flattens into a plateau-like shape well-approximated by the Thomas–Fermi model. Additionally, we show that super-Gaussian functions provide excellent fits to the ground-state density profiles, offering a simple and accurate modeling approach. To study the system’s dynamical behavior, we develop an analytical framework for quantum droplets subjected to a periodic lattice potential. In the weak-lattice limit (V_0rightarrow 0), the excitation spectrum reveals a Goldstone gapless phonon mode, characteristic of superfluidity. However, at low densities, the inclusion of Lee–Huang–Yang corrections leads to phonon instabilities, consistent with the transition from a peak- to a plateau-like ground state. In the strong-lattice regime (large V_0), a gap opens in the lowest excitation modes, suggesting a crossover from a superfluid to a Mott-insulating phase. Our findings should shed light on key aspects of a low-dimensional quantum droplet.

We study the partitioning of motile bacteria in an aqueous two-phase mixture of dextran (DEX) and polyethylene glycol (PEG), which can phase separate into DEX-rich and PEG-rich phases. While nonmotile bacteria partition exclusively into the DEX-rich phase in all conditions tested, we observed that motile bacteria penetrate the soft DEX-PEG interface and partition variably among the two phases. For our model organism Bacillus subtilis, the fraction of motile bacteria in the DEX-rich phase increased from 0.58 to 1 as we increased the DEX composition within the two-phase region. We hypothesized that the chemical affinity between DEX and the bacteria cell wall acts to weakly confine the bacteria within the DEX-rich phase; however, motility can generate sufficient mechanical forces to overcome the soft confinement and propel the bacteria into the PEG-rich phase. Using optical tweezers to drag a bacterium across the DEX-PEG interface, we demonstrate that the overall bacteria partitioning is determined by a competition between the interfacial forces and bacterial propulsive forces. Our measurements are supported by a theoretical model of dilute active rods embedded within a periodic soft confinement potential.

Exciton-to-trion conversion in two-dimensional semiconductors defines the transition from an optoelectronics based on neutral bosons to one based on charged fermions, with a huge impact on the transport and spin/valley-related properties. This process has been successfully induced in field-effect transistors under gate voltage, chemically doped samples, and nonuniformly nanoscale-strained materials. Here, we study the evolution of the photoluminescence spectrum of monolayer WS2 under high pressure, decoupling exciton and trion contributions by their responses to laser-power variations. We demonstrate that crystal compression drives a substrate-independent, partially reversible exciton-to-trion conversion, with trion recombination dominating the emission above 3 GPa. The observed mechanism does not rely on external charge injection but involves the pressure evolution of intrinsic doping levels within the band structure. Our results indicate that trion-based emission can be achieved by reshaping the periodic crystal potential via the modulation of interatomic interactions, offering a novel approach to the study of exciton-to-trion conversion in two-dimensional materials.

Spherically averaged periodic pair potentials offer the enticing promise to provide accurate results at a drastically reduced computational cost compared to the traditional Ewald sum. In this work, we employ the pair potential by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)0021-960610.1063/1.1624364] in ab initio path integral Monte Carlo (PIMC) simulations of the warm dense uniform electron gas. Overall, we find very accurate results with respect to Ewald reference data for integrated properties such as the kinetic and potential energy, whereas wavenumber-resolved properties such as the static structure factor S(q), the static linear density response χ(q), and the static quadratic density response χ^{(2)}(q,0) fluctuate for small q. In addition, we perform an analytic continuation to compute the dynamic structure factor S(q,ω) from PIMC results of the imaginary-time density-density correlation function F(q,τ) for both pair potentials. Our results have important implications for future PIMC calculations, which can be sped up significantly using the Yakub and Ronchi potential for the estimation of equation-of-state properties or q-resolved observables in the noncollective regime, whereas a full Ewald treatment is mandatory to accurately resolve physical effects manifesting for smaller q, including the evaluation of compressibility sum rules, the interpretation of x-ray scattering experiments at small scattering angles, and the estimation of optical and transport properties.

Abstract Trapped ions in a periodic potential are a paradigm of a frustrated Wigner crystal. We study a model for a 1D chain of such ions, as well as an approximation by a Frenkel–Kontorova model. The FK model, however, has other long-range properties. We discuss the meaning of structures like kink or anti-kink in the frame of the soliton theory, and that ion chains with large distances against the laser frame can have difficulties to move solitons. We study the case with 3 particles only for which all important properties can be demonstrated.

The aim of this study was to evaluate liposomal particles as a potential delivery system for natamycin, a widely known antimicrobial agent used in the food industry. The goal was to prolong its diffusion into the surrounding medium. Natamycin-loaded liposomes were prepared using two methods (proliposome and thin-film) and two different phospholipid mixtures. The characterization of natamycin-loaded liposomes was performed in terms of their chemical composition (FT-IR analysis), encapsulation efficiency (EE), and antimicrobial potential against spoilage and pathogenic microorganisms that can be found in milk and milk products. During the 60-day storage period, their size, polydispersity index (PDI), and zeta potential were measured. The in vitro release kinetics of natamycin from liposomes were also assessed, and the results showed a significantly lower release rate of the drug when it was encapsulated. EE showed a high level of natamycin encapsulation (>80%), which was confirmed with FT-IR analysis. The stability study indicated that these systems were stable over a 60-day storage period, as the zeta potential of all formulations was ~−25 mV. Satisfactory antimicrobial performance of the developed liposomes against Listeria monocytogenes, Yersinia enterocolitica, Candida tropicalis, Candida parapsilosis, and Aspergillus flavus (MIC values from 0.00625 to 4 mg/mL) indicates that loading of natamycin into liposomal carriers was an adequate method for their encapsulation and delivery in the milk industry.

We investigate the overdamped directed transport of elastically coupled Brownian particles in asymmetric periodic potentials, driven by nonequilibrium fluctuations modeled as Poisson shot noise (PSN). Our findings reveal distinct modulations in the coupling effect, characterized by alternating regimes of transport enhancement, suppression, and even coupling-induced current reversal. This complex phenomenology arises from nonequilibrium fluctuations, whereas thermal equilibrium fluctuations are unable to induce net transport in the absence of external deterministic drives. Based on the discrete nature of PSN, we propose two underlying mechanisms responsible for these observed modulations: dual-mode motion and passive push-pull dynamics between coupled particles. By analyzing the velocity difference between coupled and single particles, we demonstrate that these modulations in coupling-induced transport are determined by the interplay between nonequilibrium fluctuations and the potential barrier height. Specifically, for low mean strengths of the nonequilibrium fluctuations, a characteristic three-stage pattern of coupling effects (suppression-enhancement-suppression) is observed with increasing potential barrier height. Furthermore, the interplay between the rate and average amplitude of the discrete pulses defining these nonequilibrium fluctuations also profoundly shapes the coupling effect, yielding diverse transport characteristics. Moreover, the potential's asymmetry coefficient, the noise skewness, and the interparticle coupling strength are shown to significantly modulate the coupling-induced transport. Our study establishes a theoretical framework for understanding the intricate collective transport dynamics of coupled particles driven by nonequilibrium fluctuations. These findings provide critical insights for the design and control of directed motion in artificial micro- and nanoscale systems operating under discrete energy pulses in nonequilibrium environments.