Collective Coordinates Research Articles

Correction to baryon spectrum in holographic QCD

We study solitons in the context of Sakai-Sugimoto-Witten holographic model of QCD. In the large 't Hooft coupling limit, flat space instantons give an approximate description of baryons. We provide an ansatz through deforming the BPST instanton by zero modes and obtain a subleading correction to the effective action. We also consider the quantum mechanical description of the collective coordinates. The correction term appears as a perturbation to the potential of the Hamiltonian and hence we can derive a first order correction to the mass spectrum of baryons.

The social unconscious: Then and now

AbstractThis is a brief introductory paper about the history and centrality of the social unconscious in psychoanalytic theory and practice. The term―Social Unconscious―was introduced into our literature more than 100 years ago by the first formally trained American psychoanalyst―Trigant Burrow. It opens new pathways for understanding the social and collective dimensions of the unconscious, allowing us to extend our reach with our patients and our relevance with fellow citizens. Despite its potential, the social unconscious and the theories that undergird it were denigrated by Freud. In the early 1930’s, Freud instructed the American Psychoanalytic Association to remove Trigant Burrow from its membership and to excise this scholarship from its curricula. Coordinated attempts to suppress these ideas harmed the field’s development and retarded its relevance. Understanding the social dimensions of the unconscious is necessary because the unconscious is largely structured by social, cultural and collective coordinates. Fortunately, the turn into the 21st century is seeing a proliferation in analytic scholarship regarding the centrality of the socio‐cultural in structuring the unconscious of individuals and groups. New terms are being introduced such as vinculo, normative unconscious, interpellation, semiotic code, and ego‐habitus that aim to elaborate the various ways culture, ideology, large‐groups, and geopolitical processes shape the unconscious. Their potential to deepen our contact with patients across the spectrum of human difference is immense. I suggest using the capacious term―social unconscious―as a core conceptual category that organizes this vein of expanding analytic scholarship.

Time-dependent generator coordinate method study of fission: Dissipation effects

Starting from a quantum theory of dissipation for nuclear collective motion introduced by Kerman and Koonin [Phys. Scr. 10, 118 (1974)], the time-dependent generator coordinate method (TDGCM) is extended to allow for dissipation effects in the description of induced fission dynamics. The extension is based on a generalization of the GCM generating functions that includes excited states, and the resulting equation of motion in the collective coordinates and excitation energy. With the assumption of a narrow Hamiltonian kernel, an expansion in a power series in collective momenta leads to a Schr\"odinger-like equation that explicitly includes a dissipation term, proportional to the momentum of the statistical wave function. An illustrative calculation is performed for induced fission of $^{228}\mathrm{Th}$. The three-dimensional model space includes the axially symmetric quadrupole and octupole shape variables, and the nuclear temperature. When compared with data for photoinduced fission of $^{228}\mathrm{Th}$, the calculated fission yields demonstrate the important role of the additional term in the Hamiltonian that explicitly takes into account the dissipation of energy of collective motion into intrinsic degrees of freedom.

Moving kinks and their wave packets

Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, it is currently limited to solitons which stay close to a base point, about which the theory is linearized. As a result, so far this formalism has only been applied to stationary solitons. In spite of this limitation, we construct kink states with fixed nonzero momenta and also moving, normalizable kink wave packets. The former are nonnormalizable, coherent superpositions of kinks at all spatial positions and are simultaneous eigenstates of the Hamiltonian and the momentum operator. The latter are localized about a single, moving classical solution. To understand the wave packets, we calculate several simple matrix elements.

Nudged elastic band approach to nuclear fission pathways

Background: The nuclear fission process is a dramatic example of the large-amplitude collective motion in which the nucleus undergoes a series of shape changes before splitting into distinct fragments. This motion can be represented by a pathway in the many-dimensional space of collective coordinates. Within a stationary framework rooted in a static collective Schr\"odinger equation, the collective action along the fission pathway determines the spontaneous fission half-lives as well as mass and charge distributions of fission fragments.Purpose: We study the performance and precision of various methods to determine the minimum-action and minimum-energy fission trajectories in the collective space.Methods: We apply the nudged elastic band method (NEB), grid-based methods, and the Euler-Lagrange approach to the collective action minimization in two- and three-dimensional collective spaces.Results: The performance of various approaches to the fission pathway problem is assessed by studying the collective motion along both analytic energy surfaces and realistic potential-energy surfaces obtained with the Skyrme-Hartree-Fock-Bogoliubov theory. The uniqueness and stability of the solutions is studied. The NEB method is capable of efficient determination of the exit points on the outer turning surface that characterize the most probable fission pathway and constitute the key input for fission studies. This method can also be used to accurately compute the critical points (i.e., local minima and saddle points) on the potential-energy surface of the fissioning nucleus that determine the static fission path. The dynamic programming method also performs quite well and it can be used in many-dimensional cases to provide initial conditions for the NEB calculations.Conclusions: The NEB method is the tool of choice for finding the least-action and minimum-energy fission trajectories. It will be particularly useful in large-scale static fission calculations of superheavy nuclei and neutron-rich fissioning nuclei contributing to the astrophysical $r$-process recycling.

Recognition and Binding of RsmE to an AGGAC Motif of RsmZ: Insights from Molecular Dynamics Simulations.

CsrA/RsmE is a post-transcriptional regulator protein widely distributed in bacteria. It impedes the expression of target mRNAs by attaching their 5' untranslated region. The translation is restored by small, noncoding RNAs that sequester CsrA/RsmE acting as sponges. In both cases, the protein recognizes and attaches to specific AGGAX and AXGGAX motifs, where X refers to any nucleotide. RsmZ of Pseudomonas protegens is one of these small RNAs. The structures of some of its complexes with RsmE were disclosed a few years ago. We have used umbrella sampling simulations to force the unbinding of RsmE from the AGGAC motif located in the single-stranded region sited between stem loops 2 and 3 of RsmZ. The calculations unveiled the identity of the main residues and nucleotides involved in the process. They also showed that the region adopts a hairpin-like conformation during the initial stages of the binding. The ability to acquire this conformation requires that the region has a length of at least nine nucleotides. Besides, we performed standard molecular dynamics simulations of the isolated fragments, analyzed their typical conformations, and characterized their movements. This analysis revealed that the free molecules oscillate along specific collective coordinates that facilitate the initial stages of the binding. The results strongly suggest that the flexibility of the single-stranded region of RsmZ crucially affects the ability of its binding motif to catch RsmE.

Generator coordinate method for transition-state dynamics in nuclear fission

Since its beginnings, fission theory has assumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Nevertheless, up to now there is no microscopic theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configuration-interaction framework using the generator coordinate method (GCM). Simple reaction-theoretic models are constructed with the Gaussian overlap approximation to parametrize both the dynamics within the channels and their incoherent couplings to states outside the barrier. The physical characteristics of the channels examined here are their effective bandwidths and the quality of the coupling to compound-nucleus states as measured by the transmission factor $T$. We also investigate the spacing of GCM states with respect to their degree of overlap. We find that a rather coarse mesh provides an acceptable accuracy for estimating the bandwidths and transmission factors. The common numerical stability problem in using the GCM is avoided due to the choice of meshes and the finite bandwidths of the channels. The bandwidths of the channels are largely controlled by the zero-point energy with respect to the collective coordinate in the GCM configurations.

Relativistic moduli space for kink collisions

The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by expanding the Derrick scaling parameter about unity and treating the higher-order Derrick modes as new degrees of freedom. This approach allows us to resolve (coordinate) singularities order-by-order, and systematically incorporates relativistic corrections {\it perturbatively} in kink scattering. It gives an excellent description of kink-antikink collisions in $\phi^4$ field theory already at first order, and at higher order, reproduces the fractal structure in the formation of the final state with an error of only $4\%$.

Collective bath coordinate mapping of "hierarchy" in hierarchical equations of motion.

The theory of hierarchical equations of motion (HEOM) is one of the standard methods to give exact evaluations of the dynamics as coupled to harmonic oscillator environments. However, the theory is numerically demanding due to its hierarchy, which is the set of auxiliary elements introduced to capture the non-Markovian and non-perturbative effects of environments. When system-bath coupling becomes relatively strong, the required computational resources and precision move beyond the regime that can be currently handled. This article presents a new representation of HEOM theory in which the hierarchy is mapped into a continuous space of a collective bath coordinate and several auxiliary coordinates as the form of the quantum Fokker-Planck equation. This representation gives a rigorous time evolution of the bath coordinate distribution and is more stable and efficient than the original HEOM theory, particularly when there is a strong system-bath coupling. We demonstrate the suitability of this approach to treat vibronic system models coupled to environments.

Microscopic collective inertial masses for nuclear reaction in the presence of nucleonic effective mass

Collective inertial mass coefficients with respect to translational, relative, and rotational motions are microscopically calculated, along the collective reaction path self-consistently determined, based on the adiabatic self-consistent collective coordinate (ASCC) method. The impact of the time-odd component of the mean-field potential on the inertial masses are investigated. The results are compared with those calculated with the cranking formulae. The inertial masses based on the ASCC method reproduce the exact total nuclear mass for the translational motion as well as the exact reduced masses as the asymptotic values for the relative and rotational motions. In contrast, the cranking formulae fail to do so. This is due to the fact that the (local) Galilean invariance is properly restored in the ASCC method, but violated in the cranking formulae. A model Hamiltonian for low-energy nuclear reaction is constructed with the microscopically derived potentials and inertial masses. The astrophysical S-factors are calculated, which indicates the importance of microscopic calculation of proper inertial masses.

Multi-Raman soliton self-frequency shifts and dissipative rogue wave trains induced by cubic-quintic-Raman contributions in a double-negative material

We examine the cubic-quintic-Raman influences on the system when the second-order dispersion and the cubic-quintic-nonlinearities act in a double-negative material. This research is done for both absorption and negative index regimes. Using the collective coordinates’ technique, the quintic-nonlinearity induces the generation of Kuznetsov-Ma breathers and Peregrine soliton. Thereafter, the cubic-Raman effect comes into play and breeds the chaotic Peregrine waves’ field, the complex rogue event, and the modified complex rogue event. Therefore, the quintic-Raman effect induces first-, second-, and third-forms of the dissipative rogue waves and the twin parallel wave trains. Some fascinating phenomena such as deletion of waves, damping effect, tree structure, and disintegration of the Raman soliton self-frequency shift leading to the multi-Raman soliton self-frequency shifts, are also scrutinized. Further, internal strife leading to these above-mentioned effects, are likewise presented in detail.

The prediction of protein–ligand unbinding for modern drug discovery

Introduction Drug–target thermodynamic and kinetic information have perennially important roles in drug design. The prediction of protein–ligand unbinding, which can provide important kinetic information, in experiments continues to face great challenges. Uncovering protein–ligand unbinding through molecular dynamics simulations has become efficient and inexpensive with the progress and enhancement of computing power and sampling methods. Areas covered In this review, various sampling methods for protein–ligand unbinding and their basic principles are firstly briefly introduced. Then, their applications in predicting aspects of protein–ligand unbinding, including unbinding pathways, dissociation rate constants, residence time and binding affinity, are discussed. Expert opinion Although various sampling methods have been successfully applied in numerous systems, they still have shortcomings and deficiencies. Most enhanced sampling methods require researchers to possess a wealth of prior knowledge of collective variables or reaction coordinates. In addition, most systems studied at present are relatively simple, and the study of complex systems in real drug research remains greatly challenging. Through the combination of machine learning and enhanced sampling methods, prediction accuracy can be further improved, and some problems encountered in complex systems also may be solved.

Study of pulsed radiation by the collective coordinates method

We examine the feasibility of analyzing the behavior of a radiating pulse during its propagation in an optical fiber transmission line by the collective coordinates approach. We show that once the waves radiation are created, their dynamics is well described by the variational equations. We also show that, these waves of radiation do not keep a constant profile during their propagation, but are spread out continuously. Their frequency remains constant and is compared to the carrying frequency at a variation ranging between GHz and THz. The precise knowledge of the frequency or the temporal position of the radiation allows us to consider the possibility of removing the radiation in one operation by spectral or temporal filtering.

Development of anharmonic vibrational structure theory using backflow transformation

A backflow (BF) transformation was applied to a vibrational self-consistent field wavefunction, which is the mean-field approximation in an anharmonic vibrational structure theory. We tested its effectiveness on the H2O molecule using quantum Monte Carlo method. Each normal mode coordinate was transformed into collective coordinates using the correlation function depending on whole coordinates. The vibrational frequencies with the BF transformation reasonably agree with the vibrational configuration interaction (VCI) results. The vibrational probability density to which the BF transformation was applied was also consistent with the VCI results and showed that the BF transformation appropriately take into account the inter-mode couplings.

IRA: A Shape Matching Approach for Recognition and Comparison of Generic Atomic Patterns.

We propose a versatile, parameter-less approach for solving the shape matching problem, specifically in the context of atomic structures when atomic assignments are not known a priori. The algorithm Iteratively suggests Rotated atom-centered reference frames and Assignments (iterative rotations and assignments (IRA)). The frame for which a permutationally invariant set-set distance, namely, the Hausdorff distance, returns a minimal value is chosen as the solution of the matching problem. IRA is able to find rigid rotations, reflections, translations, and permutations between structures with different numbers of atoms, for any atomic arrangement and pattern, periodic or not. When distortions are present between the structures, optimal rotation and translation are found by further applying a standard singular value decomposition-based method. To compute the atomic assignments under the one-to-one assignment constraint, we develop our own algorithm, constrained shortest distance assignments (CShDA). The overall approach is extensively tested on several structures, including distorted structural fragments. The efficiency of the proposed algorithm is shown as a benchmark comparison against two other shape matching algorithms. We discuss the use of our approach for the identification and comparison of structures and structural fragments through two examples: a replica-exchange trajectory of a cyanine molecule, in which we show how our approach could aid the exploration of relevant collective coordinates for clustering the data, and a SiO2 amorphous model, in which we compute distortion scores, and compare them with a classical strain-based potential. The source code and benchmark data are available at https://github.com/mammasmias/IterativeRotationsAssignments.

ϕ4 kink mass at two loops

The two-loop correction to the mass of the $\phi^4$ kink is $0.0126\lambda/m$ in terms of the coupling $\lambda$ and the meson mass $m$ evaluated at the minimum of the potential. This is calculated using a recently proposed alternative to collective coordinates. Both the kink energy and the vacuum energy are IR divergent at this order. To cancel the divergence, the two energy densities are subtracted before integrating over space, or equivalently a finite counterterm is added to the Hamiltonian density to cancel the vacuum energy density. All spatial integrals are performed analytically. However in the last step of our calculation, integrals over virtual momenta are performed numerically.

Microscopic self-consistent description of induced fission: Dynamical pairing degree of freedom

The role of dynamical pairing in induced fission dynamics is investigated using the time-dependent generator coordinate method in the Gaussian overlap approximation, based on the microscopic framework of nuclear energy density functionals. A calculation of fragment charge yields for induced fission of $^{228}$Th is performed in a three-dimensional space of collective coordinates that, in addition to the axial quadrupole and octupole intrinsic deformations of the nuclear density, also includes an isoscalar pairing degree of freedom. It is shown that the inclusion of dynamical pairing has a pronounced effect on the collective inertia, the collective flux through the scission hyper-surface, and the resulting fission yields, reducing the asymmetric peaks and enhancing the contribution of symmetric fission, in better agreement with the empirical trend.

Statistical analysis of correlations in the x-ray induced Coulomb explosion of iodopyridine

Coulomb explosion imaging is a promising experimental tool to study individual molecules. In this work simulation data for the x-ray induced Coulomb explosion of 2-iodopyridine is analyzed and the involved fragmentation dynamics are described. It is found that particular final ion momenta show correlations that reflect a collision of two atoms during the explosion. Variations of the proton kinetic energies can be associated with variations in the charge build-up time. Covariances of the forces during the explosion can be utilized to simplify the description of the dynamics in reduced dimensionality using only four collective coordinates.

Axion Mass from Magnetic Monopole Loops.

We show that axions interacting with Abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their energy spectrum. The axion potential can also be understood as a type of instanton effect due to a Euclidean monopole worldline winding around its dyon collective coordinate. We calculate this effect, which has features in common with both non-Abelian instantons and Euclidean brane instantons. To provide consistency checks, we argue that this axion potential vanishes in the presence of a massless charged fermion and that it is robust against the presence of higher-derivative corrections in the effective Lagrangian. Finally, as a first step toward connecting with particle phenomenology and cosmology, we discuss the regime in which this potential is important in determining the dark matter relic abundance in a hidden sector containing an Abelian gauge group, monopoles, and axions.

Soliton dynamics in the ABS nonlinear spinor model with external fields

We consider the novel nonlinear model in (1 + 1)-dimensions for Dirac spinors recently introduced by Alexeeva et al (Ann. Phys., NY 403 198) (ABS model), which admits an exact explicit solitary-wave (soliton for short) solution. The charge, the momentum, and the energy of this solution are conserved. We investigate the dynamics of the soliton subjected to several potentials: a ramp, a harmonic, and a periodic potential. We develop a collective coordinates (CCs) theory by making an ansatz for a moving soliton where the position, rapidity, and momentum, are functions of time. We insert the ansatz into the Lagrangian density of the model, integrate over space and obtain a Lagrangian as a function of the CCs. This Lagrangian differs only in the charge and mass with the Lagrangian of a CCs theory for the Gross–Neveu equation. Thus the soliton dynamics in the Alexeeva–Barashenkov–Saxena (ABS) spinor model is qualitatively the same as in the Gross–Neveu equation, but quantitatively it differs. These results of the CCs theory are confirmed by simulations, i.e. by numerical solutions for solitons of the ABS spinor model, subjected to the above potentials.