Internal Degrees Of Freedom Research Articles

The Metric Structure of Nucleic Acids and the Higher Dimension of Their Constituents

The purpose of the study is to build a metric model of the structure of a nucleic acid molecule, taking into account the higher dimension of its components, the actual lengths of chemical bonds, and the angles between them. Calculations by the constructed model showed the closeness of the known experimental characteristic parameters of the nucleic acid (helix diameter, period length) and the calculated values of these parameters. The internal degree of freedom of the nucleic acid molecule is revealed: the angle of rotation of the phosphoric acid residue relative to the chemical bond connecting it to the five-carbon sugar molecule. It is established that the value of this angle determines the shape of the nucleic acid molecule. It is claimed that the process of transmission of hereditary information and protein synthesis occurs in a space of high dimensionality in ribosomes.

Going beyond the first Chern number

Quantum Simulation Topological properties of physical systems are reflected in so-called Chern numbers: A nonzero Chern number typically means that a system is topologically nontrivial. Sugawa et al. engineered a cold atom system with a nonzero second Chern number, in contrast to condensed matter physics, where only the first Chern number is usually invoked. The exotic topology relates to the emergence of a type of magnetic monopole called the Yang monopole (known from theoretical high-energy physics) in a five-dimensional space of internal degrees of freedom in a rubidium Bose-Einstein condensate. The results illustrate the potential of cold atoms physics to simulate high-energy phenomena. Science , this issue p. [1429][1] [1]: /lookup/doi/10.1126/science.aam9031

Interfacial Properties of Tetrahydrofuran and Carbon Dioxide Mixture from Computer Simulation

We determined the interfacial properties of the tetrahydrofuran + carbon dioxide (THF + CO2) binary mixture from direct simulation of the vapor–liquid interface. We consider two different models of THF based on the transferable parameters for phase equilibria-united atom (TraPPE-UA) version approach. In the first case, we use the original (flexible) TraPPE-UA model force field for the ether [J. Phys. Chem. B 2012, 115, 11234]. The second model is a planar, rigid, and approximated TraPPE-UA model recently proposed by us [J. Chem. Phys. 2016, 144, 144702]. It is demonstrated that the sophisticated flexible model does not have an overall advantage in comparison with the simplified planar model. Indeed, both models are able to predict the phase behavior and interfacial tension of pure THF with high accuracy in a wide range of temperatures and pressures. It is noticed that the planar model is faster for simulation because the internal degrees of freedom are frozen (neither bending nor torsional intramolecular ...

Paradoxically, Most Flexible Ligand Binds Most Entropy-Favored: Intriguing Impact of Ligand Flexibility and Solvation on Drug–Kinase Binding

Biophysical parameters can accelerate drug development; e.g., rigid ligands may reduce entropic penalty and improve binding affinity. We studied systematically the impact of ligand rigidification on thermodynamics using a series of fasudil derivatives inhibiting protein kinase A by crystallography, isothermal titration calorimetry, nuclear magnetic resonance, and molecular dynamics simulations. The ligands varied in their internal degrees of freedom but conserve the number of heteroatoms. Counterintuitively, the most flexible ligand displays the entropically most favored binding. As experiment shows, this cannot be explained by higher residual flexibility of ligand, protein, or formed complex nor by a deviating or increased release of water molecules upon complex formation. NMR and crystal structures show no differences in flexibility and water release, although strong ligand-induced adaptations are observed. Instead, the flexible ligand entraps more efficiently water molecules in solution prior to protein binding, and by release of these waters, the favored entropic binding is observed.

Fractional Quantum Hall Effect in n = 0 Landau Band of Graphene with Chern Number Matrix

Fully taking into account of the honeycomb lattice structure, fractional quantum Hall states of graphene are considered by a pseudopotential projected into the n = 0 Landau band. By using a chirality as an internal degree of freedom, the Chern number matrices are defined and evaluated numerically. Quantum phase transition induced by changing a range of the interaction is demonstrated which is associated with chirality ferromagnetism. The chirality-unpolarized ground state is consistent with the Halperin 331 state of the bilayer quantum Hall system.

Floquet topological phases in a spin- 1/2 double kicked rotor

The double kicked rotor model is a physically realizable extension of the paradigmatic kicked rotor model in the study of quantum chaos. Even before the concept of Floquet topological phases became widely known, the discovery of the Hofstadter butterfly spectrum in the double kicked rotor model [J. Wang and J. Gong, Phys. Rev. A 77, 031405 (2008)] already suggested the importance of periodic driving to the generation of unconventional topological matter. In this work, we explore Floquet topological phases of a double kicked rotor with an extra spin-1/2 degree of freedom. The latter has been experimentally engineered in a quantum kicked rotor recently by loading Rb87 condensates into a periodically pulsed optical lattice. Under the on-resonance condition, the spin-1/2 double kicked rotor admits fruitful topological phases due to the interplay between its external and internal degrees of freedom. Each of these topological phases is characterized by a pair of winding numbers, whose combination predicts the number of topologically protected 0 and \pi-quasienergy edge states in the system. Topological phases with arbitrarily large winding numbers can be easily found by tuning the kicking strength. We discuss an experimental proposal to realize this model in kicked Rb87 condensates, and suggest to detect its topological invariants by measuring the mean chiral displacement in momentum space.

Cover: Journal of the Chinese Chemical Society 6/2018

This invited review summarizes the long way from the idea to attach a helium atom to cold molecular ions as sensor to its routine use in cryogenic rf ion traps. In the last 25 years, He buffer gas cooling became a very efficient and rather general method for getting all internal degrees of freedom into equilibrium with the cold bath gas. Using, in addition, ion traps, low enough temperatures, and high enough densities, He–M+ complexes can be formed now routinely from all kind of mass selected M+ ions. These techniques opened up many possibilities for studying the structure and reactivity of charged objects. Meanwhile vibrational predissociation spectroscopy in the fingerprint region has evolved as a routine method in analytical chemistry. More details will be discussed by Dr. Dieter Gerlich on page 629~801 in this issue. image

Signatures of Indistinguishability in Bosonic Many-Body Dynamics.

The dynamics of bosons in generic multimode systems, such as Bose-Hubbard models, are not only determined by interactions among the particles, but also by their mutual indistinguishability manifested in many-particle interference. We introduce a measure of indistinguishability for Fock states of bosons whose mutual distinguishability is controlled by an internal degree of freedom. We demonstrate how this measure emerges both in the noninteracting and interacting evolution of observables. In particular, we find an unambiguous relationship between our measure and the variance of single-particle observables in the noninteracting limit. A nonvanishing interaction leads to a hierarchy of interaction-induced interference processes, such that even the expectation value of single-particle observables is influenced by the degree of indistinguishability.

Motion Control and Optical Interrogation of a Levitating Single Nitrogen Vacancy in Vacuum.

Levitation optomechanics exploits the unique mechanical properties of trapped nano-objects in vacuum to address some of the limitations of clamped nanomechanical resonators. In particular, its performance is foreseen to contribute to a better understanding of quantum decoherence at the mesoscopic scale as well as to lead to novel ultrasensitive sensing schemes. While most efforts have focused so far on the optical trapping of low-absorption silica particles, further opportunities arise from levitating objects with internal degrees of freedom, such as color centers. Nevertheless, inefficient heat dissipation at low pressures poses a challenge because most nano-objects, even with low-absorption materials, experience photodamage in an optical trap. Here, by using a Paul trap, we demonstrate levitation in vacuum and center-of-mass feedback cooling of a nanodiamond hosting a single nitrogen-vacancy center. The achieved level of motion control enables us to optically interrogate and characterize the emitter response. The developed platform is applicable to a wide range of other nano-objects and represents a promising step toward coupling internal and external degrees of freedom.

Matrix product state description of Halperin states

Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact Matrix Product States (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wavefunctions, the Halperin states. These latest can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wavefunction symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation length which are compared to plasma analogy arguments.

Measuring the internal temperature of a levitated nanoparticle in high vacuum

The interaction of an object with its surrounding bath can lead to a coupling between the object's internal degrees of freedom and its center-of-mass motion. This coupling is especially important for nanomechanical oscillators, which are amongst the most promising systems for preparing macroscopic objects in quantum mechanical states. Here we exploit this coupling to derive the internal temperature of a levitated nanoparticle from measurements of its center-of-mass dynamics. For a laser-trapped silica particle in high vacuum we find an internal temperature of $1000(60)\,\mathrm{K}$. The measurement and control of the internal temperature of nanomechanical oscillators is of fundamental importance because blackbody emission sets limits to the coherence of macroscopic quantum states.

Summability of Connected Correlation Functions of Coupled Lattice Fields

We consider two nonindependent random fields $\psi$ and $\phi$ defined on a countable set $Z$. For instance, $Z={\mathbb Z}^d$ or $Z={\mathbb Z}^d\times I$, where $I$ denotes a finite set of possible "internal degrees of freedom" such as spin. We prove that, if the cumulants of both $\psi$ and $\phi$ are $\ell_1$-clustering up to order $2 n$, then all joint cumulants between $\psi$ and $\phi$ are $\ell_2$-summable up to order $n$, in the precise sense described in the text. We also provide explicit estimates in terms of the related $\ell_1$-clustering norms, and derive a weighted $\ell_2$-summation property of the joint cumulants if the fields are merely $\ell_2$-clustering. One immediate application of the results is given by a stochastic process $\psi_t(x)$ whose state is $\ell_1$-clustering at any time $t$: then the above estimates can be applied with $\psi=\psi_t$ and $\phi=\psi_0$ and we obtain uniform in $t$ estimates for the summability of time-correlations of the field. The above clustering assumption is obviously satisfied by any $\ell_1$-clustering stationary state of the process, and our original motivation for the control of the summability of time-correlations comes from a quest for a rigorous control of the Green-Kubo correlation function in such a system. A key role in the proof is played by the properties of non-Gaussian Wick polynomials and their connection to cumulants.

A new incompatible mode element with selective mass scaling for saturated soil dynamics

It is a well-known fact that addressing hydromechanical problems in saturated soils with the finite element method and equal-order interpolation formulations in displacements and pore pressures produces unstable results. Classically, stabilization has been achieved by increasing the interpolation degree of displacement with respect to pore pressure, hence fulfilling the Babuska–Brezzi condition. However, the use of quadratic elements involves high computational costs. From that point of view, the use of stabilized low-order elements is a more desirable option. Much research has been carried out in different directions in the stabilization of low-order formulations for saturated soils in quasistatic conditions, among others with the technique based on strain field enhancement through internal degrees of freedom. This article presents an alternative displacement–pore pressure formulation for saturated soil dynamics based on the enhancement of the displacement field through incompatible modes.

Dynamically generated patterns in dense suspensions of active filaments.

We use Langevin dynamics simulations to study dynamical behavior of a dense planar layer of active semiflexible filaments. Using the strength of active force and the thermal persistence length as parameters, we map a detailed phase diagram and identify several nonequilibrium phases in this system. In addition to a slowly flowing melt phase, we observe that, for sufficiently high activity, collective flow accompanied by signatures of local polar and nematic order appears in the system. This state is also characterized by strong density fluctuations. Furthermore, we identify an activity-driven crossover from this state of coherently flowing bundles of filaments to a phase with no global flow, formed by individual filaments coiled into rotating spirals. This suggests a mechanism where the system responds to activity by changing the shape of active agents, an effect with no analog in systems of active particles without internal degrees of freedom.

Nonequilibrium Green’s Functions in the Atomic Representation and the Problem of Quantum Transport of Electrons Through Systems With Internal Degrees of Freedom

We develop the theory of quantum transport of electrons through systems with strong correlations between fermionic and internal spin degrees of freedom. The atomic representation for the Hamiltonian of a device and nonequilibrium Green’s functions constructed using the Hubbard operators allow overcoming difficulties in the perturbation theory encountered in the traditional approach because of a larger number of bare scattering amplitudes. Representing the matrix elements of effective interactions as a superposition of terms each of which is split in matrix indices, we obtain a simple method for solving systems of very many equations for nonequilibrium Green’s functions in the atomic representation. As a result, we obtain an expression describing the electron currents in a device one of whose sites is in tunnel coupling with the left contact and the other, with the right contact. We derive closed kinetic equations for the occupation numbers under conditions where the electron flow leads to significant renormalization of them.

Gravitational attraction until relativistic equipartition of internal and translational kinetic energies

Translational ordering of the internal kinematic chaos provides the Special Relativity referents for the geodesic motion of warm thermodynamical bodies. Taking identical mathematics, relativistic physics of the low speed transport of time-varying heat-energies differs from Newton's physics of steady masses without internal degrees of freedom. General Relativity predicts geodesic changes of the internal heat-energy variable under the free gravitational fall and the geodesic turn in the radial field center. Internal heat variations enable cyclic dynamics of decelerated falls and accelerated takeoffs of inertial matter and its structural self-organization. The coordinate speed of the ordered spatial motion takes maximum under the equipartition of relativistic internal and translational kinetic energies. Observable predictions are discussed for verification/falsification of the principle of equipartition as a new basic for the ordered motion and self-organization in external fields, including gravitational, electromagnetic, and thermal ones.

Active vs. spectator modes in nonadiabatic photodissociation dynamics of the hydroxymethyl radical via the 22A(3s) Rydberg state.

The choice of the active degrees of freedom (DOFs) is a pivotal issue in a reduced-dimensional model of quantum dynamics when a full-dimensional one is not feasible. Here, several five-dimensional (5D) models are used to investigate the nonadiabatic photodissociation dynamics of the hydroxymethyl (CH2OH) radical, which possesses nine internal DOFs, in its lowest absorption band. A normal-mode based scheme is used to identify the active and spectator modes, and its predictions are confirmed by 5D quantum dynamical calculations. Our results underscore the important role of the CO stretching mode in the photodissociation dynamics of CH2OH, originating from the photo-induced promotion of an electron from the half-occupied π*CO antibonding orbital to a carbon Rydberg orbital.

Equivalence principle for quantum systems: dephasing and phase shift of free-falling particles

We ask the question of how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This inquiry is necessary because even elementary concepts like a classical trajectory are not well defined in quantum physics—trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. From this investigation we posit two logically and operationally distinct statements of the equivalence principle for quantum systems. Version A: the probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Both statements apply to all quantum states, including those without a classical correspondence, and also for composite particles with quantum internal dof.We also investigate the consequences of the interaction between internal and external dof induced by free fall. For a class of initial states, we find dephasing occurs for the translational dof, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. We also find a gravitational phase shift in the reduced density matrix of the internal dof that does not depend on the particle’s mass. For classical states, the phase shift has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation.

A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics

We consider, as a simple model problem, the application of virtual element methods (VEMs) to the linear magnetostatic three-dimensional problem in the formulation of Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming (0-forms), $H(curl)$-conforming (1-forms), and $H(div)$-conforming (2-forms) functional spaces in three dimensions, and they could surely be useful for other problems and in more general contexts.

Accuracy improvement of XFEM using Wilson's incompatible element technique

ABSTRACTBased on the extended finite element method (XFEM) and Wilson incompatible element technique, an incompatible extended finite element method (IXFEM) is presented to deal with the cracked bending problems in this study. The additional displacement modes of Wilson's incompatible element are introduced into the approximation of the XFEM. The internal degrees of freedom induced by additional models are condensed to improve efficiency. Derivation of the equilibrium equations of the IXFEM is performed. Several examples are employed to validate the capabilities of the proposed method. The influence of bending degree on the performance of proposed method is studied by changing the crack length. The numerical results indicate that the stress and displacement solutions of the IXFEM show a slight oscillation. The IXFEM achieves better convergence rate and computational accuracy compared with the traditional XFEM for the bending problems.