We present an influence functional path integral framework for treating the coupled dynamics of solvated proton and electron transfer within a nonequilibrium open system. This method formulates a generalized Langevin equation describing dynamics in systems where proton is simultaneously coupled to fermionic (metal electrons) and bosonic (solvent phonons) reservoirs. It accounts for multiple dissipative channels without relying on phenomenological assumptions. With this scheme, we capture the relaxation of oscillations associated with large quantum zero-point fluctuations when protons are trapped in a harmonic potential. When the proton's translational motion is slow, the dynamics become effectively Markovian. In this regime, dissipation to the electronic reservoir is characterized by a position-dependent electronic friction. Using an effective electronic model Hamiltonian, we demonstrate that electronic friction introduces a sharp, localized resistance when the proton level crosses the Fermi level, effectively delaying the reaction. In contrast, solvent friction arising from assumed Caldeira-Leggett-type coupling, exerts a uniform, position-independent drag. Both mechanisms contribute comparable amounts to the overall energy dissipation. This framework offers a computationally efficient route to simulate complex electrochemical environments involving multiple dissipative baths.

Abstract The Wentzel-Kramers-Brillouin semiclassical method is formulated for quasiparticles with quartic-in-momentum dispersion which presents the simplest case of a soft energy-momentum dispersion. It is shown that matching wave functions in the classically
forbidden and allowed regions requires the consideration of higher-order Airy-type functions. The asymptotics of these functions are
found by using the method of steepest descents and contain additional exponentially suppressed contributions known as hyperasymptotics. These hyperasymptotics are crucially important for the correct matching of wave functions in vicinity of turning points for higher-order differential equations. A quantization condition for bound state energies is obtained, which generalizes the standard
Bohr-Sommerfeld quantization condition for particles with quadratic energy-momentum dispersion and contains non-perturbative in $\hbar$ correction. This non-perturbative correction, usually associated with tunneling effects or the presence of complex turning points, occurs even for the harmonic potential with quartic dispersion where complex turning points and tunneling are absent. The quantization condition is used to find bound state energies in the case of quadratic and quartic potentials.

Almost reducibility and growth of Sobolev norms of 1−d quantum harmonic oscillator with polynomial time quasi-periodic perturbations

Lyapunov stability and exponential phase-locking of Schrödinger–Lohe quantum oscillators

The ultrafast electronic relaxation dynamics of tetrakis(dimethylamino)ethylene (TDMAE) following photoexcitation at ∼267 nm is investigated using the time-, angle- and kinetic-energy-resolved photoelectron spectroscopy method, since we are motivated by the experimental findings in a previous similar study (E. Gloaguen et al., J. Am. Chem. Soc., 2005, 127, 16529-16534). Based on the detailed analysis of the current high-quality data, the lifetime of the initially prepared ππ* state is found to be 50 ± 10 fs and it is clearly evident that an intermediate Rydberg state with a lifetime of 550 ± 50 fs plays a pivotal role in the photodynamics of TDMAE. In addition, a partial wave packet revival is also observed with a period of ∼500 fs. This coherent oscillation, which is attributed to a vibrational quantum beat associated with overtones of the low-frequency C-C twist vibration in TDMAE, survives the ultrafast internal conversion processes and finally damps on a time scale of the order of several picoseconds.

The reaction of ammonium pertechnetate, (NH4)(TcO4), with SO3 leads to crystals of (NH4)2[Tc2O2(S2O7)4] (monoclinic, P21/c, Z= 2, a= 775.67(5), b= 1339.55(8), c= 1233.32(8) pm, β = 100.566(2)°). The compound contains the dimeric [Tc2O2(S2O7)4]2- anion with the Tc atom connected by disulfate anions. It is astonishing that even under the oxidizing reaction conditions, reduction of the Tc(VII) starting material occurs. Contrastingly, an analogous reaction of (NH4)(ReO4) with SO3 gives the Re(VII) sulfate (NH4)[ReO2(S2O7)2] (orthorhombic, Pca21, Z= 8, a= 1842.7(1), b= 847.03(5), c= 1663.8(1) pm). The compounds have been further studied by vibrational spectroscopy and quantum mechanical calculations.

In this article, investigates the interactions of the Dirac oscillator in the context of global monopoles, focusing on the effects of fermionic fields in curved spacetime. By analyzing the Dirac equation and employing a partition function, we derive essential thermodynamic properties such as Helmholtz free energy, average energy, entropy, and heat capacity. The results reveal that variations in the topological defect parameter and angular frequency significantly influence these properties, affecting both energy levels and information measures in position and momentum spaces. This research highlights the intricate relationship between thermodynamic behavior and quantum information, paving the way for further exploration in quantum computing applications.

Abstract Controlling heat flow at the quantum level is essential for the development of next-generation thermal devices. We investigate thermal rectification in a quantum harmonic oscillator coupled to two thermal baths via both single-photon (linear) and two-photon (nonlinear) exchange processes. At low temperatures, rectification emerges from a state-dependent thermal blockade: the cold bath drives the oscillator into low-occupancy states, suppressing two-photon emission and impeding energy flow. At higher temperatures, rectification is governed by the asymmetric scaling of higher-order moments associated with two-photon absorption and emission. We systematically explore various bath coupling configurations and identify the conditions under which nonlinear dissipation leads to directional heat flow. Furthermore, we propose an implementation scheme based on coupling an auxiliary two-level system to the oscillator, enabling effective two-photon dissipation. We also extend our analysis to three-photon processes and show that rectification increases systematically with photon interaction order. These results contribute to the understanding of quantum heat transport in the presence of nonlinear dissipation and may support future efforts in nanoscale thermal rectification design.

Atroposelective Suzuki-Miyaura cross coupling serves as a powerful synthetic approach for the direct assembly of biaryl products with axial chirality. However, theoretical understanding and prediction for atroposelectivity remain elusive because the conformational diversity is complicated. Moreover, dynamic paths deviating from the minimum energy path also contribute to the product distribution. Herein, we performed a conformation sampling workflow based on molecular dynamics simulation with a constrained harmonic potential for coordinate bonds to completely sample the conformations of transition states for the crucial reductive elimination step in the catalytic cycle. Through statistical analysis of transition states conformations, an atroposelectivity ratio of 94:6 was determined, which matches well with the experimental results (97:3 er). On the other hand, abinitio molecular dynamics simulations were utilized to explore the dynamic path on the free energy surface. We are addressing persistent challenges in modeling highly irreversible processes using current enhanced sampling methodologies. This work is expected to stimulate future investigations on the conformational diversity and dynamic effect in Pd-catalyzed atroposelective Suzuki-Miyaura cross coupling reactions.

Recent theoretical and experimental investigations have identified the formation of a previously unrecognized intermediate characterized by a strongly twisted C5=C6 double bond in the ground electronic state of pyrimidine nucleobases in an aqueous solution. This intermediate is produced by ultrafast internal conversion, representing a critical pathway in the photophysics of nucleobase relaxation. Nevertheless, the existence of such a species under gas-phase conditions has not yet been confirmed. In this study, we present the first direct experimental evidence for the formation of twisted intermediates in isolated molecules. Analysis of vibrational quantum beats observed using extreme ultraviolet time-resolved photoelectron spectroscopy reveals the presence of this transient species in the gas phase, further confirming that its formation is an intrinsic property of the nucleobase chromophore.

In view of the remarkable progress in microrheology to monitor the random motion of Brownian particles with a size as small as a few nanometers, and given that de Broglie matter waves have been experimentally observed for large molecules of comparable nanometer size, we examine whether Brownian particles can manifest a particle-wave duality without employing a priori arguments from quantum decoherence. First, we examine the case where Brownian particles are immersed in a memoryless viscous fluid with a time-independent diffusion coefficient, and the requirement for the Brownian particles to manifest a particle-wave duality leads to the untenable result that the diffusion coefficient has to be proportional to the inverse time, therefore, diverging at early times. This finding agrees with past conclusions published in the literature, that quantum mechanics is not equivalent to a Markovian diffusion process. Next, we examine the case where the Brownian particle is trapped in a harmonic potential well with and without dissipation. Both solutions of the Fokker–Planck equation for the case with dissipation, and of the Schrödinger equation for the case without dissipation, lead to the same physically acceptable result—that for the Brownian particle to manifest a particle-wave duality, its mean kinetic energy kBT/2 needs to be ½ the ground-state energy, E0=12ℏω of the quantum harmonic oscillator. Our one-dimensional calculations show that for this to happen, the trapping needs to be very strong so that a Brownian particle with mass m and radius R needs to be embedded in an extremely stiff solid with shear modulus, G proportional to m/RkBT/ℏ2.

Thermodynamic properties can, in principle, be derived from the partition function, which, in many-atom systems, is hard to evaluate as it involves a sum over the accessible microscopic states. Recently, the partition function has been computed via nested sampling, relying on Bayesian statistics, which is able to provide the density of states as a function of the energy in a single run, independently of the temperature. This appealing property is lost whenever the potential energy that appears in the partition function is temperature-dependent-for instance, in mean-field effective potential energies or the quantum partition function in the path-integral formalism. For these cases, nested sampling must be carried out at each temperature, which results in a massive increase in computational time. Here, we introduce and implement a new method based on an extended partition function where the temperature is considered an additional parameter to be sampled. The extended partition function can be evaluated by nested sampling in a single run, thereby restoring this highly desirable property even for temperature-dependent effective potential energies. We apply this original method to compute the quantum partition function for harmonic potentials and Lennard-Jones clusters at low temperatures and show that it outperforms the straightforward application of nested sampling for each temperature within several temperature ranges.

Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, we describe the relative diffusion of the spin dipoles by means of a Fokker-Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker-Planck equation for the diffusion propagator, we estimate dipole-dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)-aqua and Gd(III)-DO3A-butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen-Purcell-Pound, the Solomon-Bloembergen-Morgan, and the Hwang-Freed models. Our implementation is general and publicly available for application to a broad range of systems.

ABSTRACT We introduce and experimentally demonstrate an energy‐efficient method for holding and rearranging an array of atoms using only optical tweezers. Our approach employs a single optical tweezer that sequentially releases and recaptures individual atoms. By applying a stroboscopic harmonic potential, we maintain the phase‐space quadrature of each atom's probability distribution during this “blinking” process, provided the trap frequency meets specific conditions. In our proof‐of‐concept experiments, we show that a blinking tweezer can hold atoms using just of the optical power per atom and further facilitate rearrangement atoms in various configurations. With further technical improvements, such as ground‐state cooling and correction for trap anharmonicities, this technique is expected to be scaled up to around atoms in our setup. This method provides a scalable and reconfigurable platform for optical tweezer arrays, with potential applications in assembling and manipulating large‐scale quantum systems.

We investigate the effect of giant negative magnetoresistance in ultrahigh-mobility (μ≫107cm2V−1s−1) two-dimensional electron systems. These systems present a dramatic drop in the mangetoresistance at low magnetic fields (B∼0.1 T) and temperatures (T∼0.1 K). This effect is reversed by increasing the temperature or the presence of an in-plane magnetic field. The motivation for the present work is to develop a microscopical model to explain the experimental evidence, based on coherent states and Schródinger cat states of the quantum harmonic oscillator. Thus, we approach the giant negative magnetoresistance effect based on the description of ultrahigh-mobility two-dimensional electron systems in terms of Schrödinger cat states (superposition of coherent states of the quantum harmonic oscillator). We explain the experimental results in terms of the increasing disorder in the sample due to the rising temperature or the in-plane magnetic field, breaking up the Schrödinger cat states and giving rise to mere coherent states, which hold magnetoresistance in lower-mobility samples. The latter, jointly with the description of ultrahigh-mobility samples with Schrödinger cat states, accounts for the main contribution. The most interesting application of this novel description of such systems would be in the implementation of qubits for quantum computing based on bosonic models.

In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free from the fermion signproblem, enabling efficient simulations of fermionic systems. We found that by shifting the pseudo-fermion energy based on the energy of a non-interacting fermion system, we can efficiently and reliably infer the energy of fermionic systems in various situations, from strong quantum degeneracy to weak quantum degeneracy. We have performed numerical simulations of quantum dots confined in a two-dimensional harmonic potential and found excellent agreement with benchmark results provided by other established methods. We believe that this pseudo-fermion propagator framework opens up new possibilities for numerical simulations of fermionic systems.

Good Lie Brackets for classical and quantum harmonic oscillators

Machine learning approaches to the nonlinear Schrödinger equation with harmonic potentials and Gaussian nonlinearities

Abstract Recent observational results from the DESI collaboration reveal tensions with the standard ΛCDM model and favour a scenario in which dark energy (DE) decays over time. The DESI DR2 data also suggest that the DE equation of state (EoS) may have been phantom-like ( w < - 1) in the past, evolving to w > - 1 at present — implying a recent crossing of the phantom divide at w = - 1. Scalar field models of DE naturally emerge in ultraviolet-complete theories such as string theory, which is typically formulated in higher dimensions. In this work, we investigate a broad class of thawing scalar field models — including the simple quadratic, quartic, exponential, symmetry-breaking and axion potentials — propagating on a (4+1)-dimensional ghost-free phantom braneworld, and demonstrate that their effective EoS exhibits a phantom-divide crossing. Alongside the Hubble parameter and EoS of DE, we also analyse the evolution of the Om diagnostic, and demonstrate that the time dependence of these quantities is in excellent agreement with the DESI DR2 observations. Furthermore, we perform a comprehensive parameter estimation using Markov Chain Monte Carlo sampling, and find that the χ 2 values for all our models are remarkably close to that of the widely used CPL parametrisation — indicating that our models fit the data very well.

Intra- and inter-band optical absorption in spherical quantum dots under inversely quadratic Hellmann potential