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This study proposes a novel theoretical approach to understanding the statistical–mechanical similarities between nuclear fission phenomena and semiconductor physics. Using the Hill–Wheeler formula as a quantum mechanical distribution function and establishing its correspondence with the Fermi–Dirac distribution function, we analyzed nuclear fission processes for nine nuclides (232Th, 233U, 235U, 238U, 237Np, 239Pu, 240Pu, 242Pu, 241Am) using JENDL-5.0 data.

The quantum walk is the quantum analog of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state tomography, and its spatial coherence is demonstrated. Our system allows the observation of the quantum-to-classical transition and paves the way for applications, such as quantum cellular automata.

For the Deng-Fan potential within a moving boundary condition, the time-dependent Schrödinger equation is considered analytically. The eigenvalue equation is solved by using a combination of Pekeris and Greene-Aldrich approximations. Various time-dependent quantities including density distribution function, auto-correlation function, disequilibrium, average energy, quantum similarity, and quantum similarity index are obtained for selected eight diatomic molecules. The motion of the peak of the density function, with moving boundary condition is investigated for ground states of some diatomic molecules along with the corresponding peak values.

Continuous variable quantum key distribution (CVQKD) can be potentially implemented through seawater channels, whereas the involved oceanic turbulence has a negative effect on the maximal transmission distance of quantum communication systems. Here, we demonstrate the effects of the oceanic turbulence on the performance of the CVQKD system and suggest an implementation feasibility of the passive CVQKD through the oceanic turbulence-based channel. We achieve the channel transmittance characterized by the transmission distance and depth of the seawater. Moreover, a non-Gaussian approach is used for performance improvement while counteracting the effects of excess noises on the oceanic channel. Numerical simulations show that the photon operation (PO) unit can bring reductions of excess noise when taking into account the oceanic turbulence, and hence results in performance improvement in terms of transmission distance and depth as well. The passive CVQKD explores the intrinsic field fluctuations of a thermal source without using an active scheme and hence has a promising application in chip integration for portable quantum communications.

To enhance the performance of polyimides, novel polyimides (P1, P2, P3) were synthesized through the reaction of isophthalic dianhydride with a series of furan-based diamines. The structures and properties of these polyimides (P1, P2, P3) were analyzed through molecular dynamics and quantum chemical simulation methods, including glass transition temperature, dielectric properties, free volume, and cohesive energy density. Compared with traditional polyimides, the results showed that P1, P2, and P3 exhibited a significant increase in glass transition temperature and cohesive energy density, while their dielectric properties decreased compared to traditional PI (3.4–3.6), all falling within the range of (2.5-3.0). The free volume also decreased. However, there was no significant impact on the materials’ radial distribution functions at the atomic level.

The need to describe abrupt changes or response of nonlinear systems to impulsive stimuli is ubiquitous in applications. Also the informal use of infinitesimal and infinite quantities is still a method used to construct idealized but tractable models within the famous J. von Neumann reasonably wide area of applicability. We review the theory of generalized smooth functions as a candidate to address both these needs: a rigorous but simple language of infinitesimal and infinite quantities, and the possibility to deal with continuous and generalized function as if they were smooth maps: with pointwise values, free composition and hence nonlinear operations, all the classical theorems of calculus, a good integration theory, and new existence results for differential equations. We exemplify the applications of this theory through several models of singular dynamical systems: deduction of the heat and wave equations extended to generalized functions, a singular variable length pendulum wrapping on a parallelepiped, the oscillation of a pendulum damped by different media, a nonlinear stress–strain model of steel, singular Lagrangians as used in optics, and some examples from quantum mechanics.

Discretizing a distribution function in a phase space for an efficient quantum dynamics simulation is a non-trivial challenge, in particular for a case in which a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM), most notably by a quantum Fokker–Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we employ a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths. This model is an ideal platform not only for a periodic system but also for a non-periodic system confined by a potential. We then derive the numerically “exact” hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. As demonstrations, we numerically integrate the discrete QFPE for a 2D free rotor and harmonic potential systems in a high-temperature Markovian case using a coarse mesh with initial conditions that involve singularity.

We employ computer simulations to study the mechanical response and the associated structural transformations of porous glassy materials under cyclic pure shear deformation. The glassy samples are created via the rapid thermal quench and kinetically arrested solid gas phase separation in the athermal limit. Both the limit of high and low porosity systems are prepared by varying the average density. We consider two different strain amplitudes which correspond to near yielding and the steady state plastic flow regime. Under periodic loading, the system undergoes irreversible plastic rearrangements, leading to a gradual shift towards the lower potential energy minimum state and stress–strain hysteresis. The pore structure changes over consecutive cycles which are demonstrated in terms of pore size distribution function. With increasing shear cycle the distributions become skewed towards higher length scale as the adjacent pores coalesce and form larger pores. These results are found to be strongly dependent on the system density and the strain amplitude. Finally the evolution of the pore structure is studied by analyzing the average pore diameter with shear cycle.

The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space. Alternatively, the Husimi distribution function is positive-defined everywhere, but it does not provide the correct charge and current densities. The origin of all these difficulties is the attempt to construct a phase space within a quantum theory that does not allow well-defined (i.e. simultaneous) values of the position and momentum of an electron. In contrast, within the (de Broglie–Bohm) Bohmian theory of quantum mechanics, an electron has well-defined position and momentum. Therefore, such theory provides a natural definition of the phase space probability distribution and by construction, it is positive-defined and it exactly reproduces the charge and current densities. The Bohmian distribution function has many potentialities for quantum problems, in general, and for quantum transport, in particular, that remains unexplored.

For a quantum harmonic oscillator, an explicit expression that describes the energy distribution as a coordinate function is obtained. The presence of the energy function poles is shown for the quantum system in domains where the Wigner function has negative values.