Semiclassical results in the linear response theory

Numerical modeling of fermionic many-body quantum systems presents similar challenges across various research domains, necessitating universal tools, including state-of-the-art machine learning techniques. Here, we introduce SOLAX, a Python library designed to compute and analyze fermionic quantum systems using the formalism of second quantization. SOLAX provides a modular framework for constructing and manipulating basis sets, quantum states, and operators, facilitating the simulation of electronic structures and determining many-body quantum states in finite-size Hilbert spaces. The library integrates machine learning capabilities to mitigate the exponential growth of Hilbert space dimensions in large quantum clusters. The core low-level functionalities are implemented using the recently developed Python library JAX. Demonstrated through its application to the Single Impurity Anderson Model, SOLAX offers a flexible and powerful tool for researchers addressing the challenges of many-body quantum systems across a broad spectrum of fields, including atomic physics, quantum chemistry, and condensed matter physics.

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincaré surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy εc, for ε < εc, the system is near-integrable, and as the decrease of ε the spectrum is gradually rendered regular and finally turns into a pure Coulomb field situation. On the contrary, if ε > εc, with the increase of ε, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.

Towards accurate infrared spectral density of weak H-bonds in absence of relaxation mechanisms.

Interacting systems consisting of two rotators and a pendulum are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of unstable quasiperiodic motions in phase space is studied via the Lindstedt series regarded as a sum of Feynman graphs and studied with renormalization group techniques based on Eliasson’s work on KAM tori. The result is a strong improvement, compared to our previous results, on the domain of validity of bounds that imply existence of invariant tori, large homoclinic angles, long heteroclinic chains, and drift-diffusion in phase space.

The stochastic dynamics of a rigid inclusion constrained to move on a curved surface has many applications in biological and soft matter physics, ranging from the diffusion of passive or active membrane proteins to the motion of phoretic particles on liquid-liquid interfaces. Here we construct intrinsic Langevin equationsfor an oriented rigid inclusion on a fixed curved surface using Cartan's method of moving frames. We first derive the Hamiltonian equationsof motion for the translational and rotational momenta in the body frame. Surprisingly, surface curvature couples the linear and angular momenta of the inclusion. We then add to the Hamiltonian equationslinear friction, white noise, and arbitrary configuration-dependent forces and torques to obtain intrinsic Langevin equationsof motion in phase space. We provide the integrability conditions, made nontrivial by surface curvature, for the forces and torques to admit a potential, thus distinguishing between passive and active stochastic motion. We derive the corresponding Fokker-Planck equationin geometric form and obtain fluctuation-dissipation relations that ensure Gibbsian equilibrium. We extract the overdamped equationsof motion by adiabatically eliminating the momenta from the Fokker-Planck equation, showing how a peculiar cancellation leads to the naively expected Smoluchowski limit. The overdamped equationscan be used for accurate and efficient intrinsic Brownian dynamics simulations of passive, driven, and active diffusion processes on curved surfaces. Our work generalizes to the collective dynamics of many inclusions on curved surfaces.

The dynamic aperture experiment at the CERN Super Proton Synchrotron (SPS) was aimed at finding the relevant effects that limit single-particle stability in hadron storage rings. These effects were studied in the SPS and compared with long-term particle tracking to determine to what extent computer simulations can predict the dynamic aperture under well-known conditions. Such investigations are very important for future hadron colliders such as the Large Hadron Collider as the design of these machines relies heavily on simulations. Besides this practical goal it was of utmost interest to improve the phenomenological understanding of the intricate details of particle motion in phase space. This experiment was carried out by successive teams over a period of ten years. We summarize the techniques, results, and conclusions.

We obtain new classes of invariant solutions of the integrodifferential equations describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid. For all the solutions obtained, trajectories of particle motion in phase space are calculated. The stability of some flows is studied in a linear approximation. In several cases, the construction of solutions reduces to an integrodifferential equation of the second kind, which can be solved by the iteration method.

Colorectal cancer (CRC) is one of the leading causes of cancer-related mortality globally. The rising expenses, significant side effects, and increasing resistance to traditional CRC treatments suggest the critical need for new and more effective therapeutic options. This study explored the anticancer potential of Lannea coromandelica (Houtt.) Merr. phytocompounds targeting the promising apoptosis signal-regulatory kinase 1 (ASK1) protein using computational biology approaches including molecular docking, ADMET analysis, molecular dynamics (MD) simulation, and MM/GBSA calculations. Virtual screening of the 17 phytoconstituents identified two lead compounds: ellagic acid and physcion, with binding affinities of -9.6 kcal/mol and -9.3 kcal/mol, respectively. ADMET analysis revealed favorable pharmacokinetic, pharmacodynamic, and toxicity profiles for the lead compounds. MD simulations supported the stability and compactness of the two leads in comparison to the control drug erbitux for 200 ns. The lead compounds displayed fewer rotatable bonds compared to Erbitux, resulting in lower torsional flexibility and greater stability during the simulations. PCA-based essential dynamics analysis demonstrated highly similar global motions in phase space for both lead compounds and erbitux, indicating comparable dynamic properties. Free binding energy calculations identified ellagic acid (-69.20 kcal/mol) as the superior lead compound over physcion (-65.68 kcal/mol). These results may open new avenues for the development of novel drug candidates targeting colorectal cancer. Dhaka Univ. J. Biol. Sci. 34(1): 1-23, 2025 (January)

Directing particle transport in a two-dimensional periodic potential landscape

Generalized dynamical entropies in weakly chaotic systems

In a hydrogen-bonded chain with a symmetric double-well potential there are slow-mode kink-antikink pairs and fast-mode kink-kink pairs. However, in a hydrogen-bonded chain with an asymmetric double-well potential, there are slow-mode bell-shaped soliton-antisoliton pairs corresponding to two parallel electric dipoles and fast-mode bell-shaped soliton-soliton pairs corresponding to two antiparallel electric dipoles. Propagating in a spatial inhomogeneous chain, soliton pairs may transform from slow-mode soliton-antisoliton pairs into fast-mode soliton-soliton pairs or the converse process. For bell-shaped soliton pairs, this transformation is accompanied by a reversion of the electric dipoles in one of the two sublattices. In the case of repulsion-type impurities there is a critical velocity vcr for the incident soliton pair. If the velocity v of the incident soliton pair equals vcr, its trajectory of motion in phase space will branch while, for v<vcr, forbidden regions and allowed regions for its motion will exist.

Independent continuous periodic firing series to chaos in the 3-D Hindmarsh–Rose neuron circuit

In this Chapter, we discuss in a unified way equilibrium points, periodic orbits and their stability, which constitute local concepts of Hamiltonian dynamics together with ordered and chaotic motion, which are the concern of a more global type of analysis. Using the Fermi Pasta Ulam β (FPU − β) model as an example, we study the destabilization properties of some of its simple periodic orbits and connect them to wider aspects of the motion in phase space. We show numerically that the spectrum of positive Lyapunov exponents, characterizing a region of strong chaos, becomes invariant in the thermodynamic limit, verifying that the Kolmogorov-Sinai entropy, defined as the sum of these exponents, is an extensive property of the system. The Chapter ends with an introduction of the smaller alignment index (SALI) and the generalized alignment index (GALI) criteria for distinguishing ordered from chaotic motion.

We report in this paper the results of outer and inner valence IP calculations for the HF molecule using two different many‐body methods for the direct evaluation of energy differences. The first is the nonperturbative coupled‐cluster based linear response theory (LRT) and the second is the hermitian open‐shell many‐body perturbation theory (MBPT). A Huzinaga‐Dunning (9s5p→ 5s3p/3s) basis has been used. LRT uses an “ionization operator” S as in the equation of motion method (EOM) to generate the ionized states from a coupled‐cluster type of ground state. S is chosen to consist of single ionization and ionization‐cum‐shake‐up operators, thus treating the Koopmans as well as the shake‐up states on equal footing. LRT would thus be capable of computing both the outer and the inner valence regions with equal facility. This is borne out by the results. For the open‐shell MBPT, the model space is chosen to be spanned by the singly ionized determinants. The convergence of the results for the inner valence region is slow, and the results obtained from the [2, 1] Pade' approximants are presented. Unlike the LRT, the inner valence region is not reproduced with full complexity in MBPT, indicating that it is essential to modify the theory by way of expanding the model space to contain the shake‐up determinants also.