Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Spontaneous local symmetry breaking: a conformational study of glycine on Cu{311}

Understanding the interplay between intrinsic molecular chirality and chirality of the bonding footprint is crucial in exploiting enantioselectivity at surfaces. As such, achiral glycine and chiral alanine are the most obvious candidates if one is to study this interplay on different surfaces. Here, we have investigated the adsorption of glycine on Cu{311} using reflection-absorption infrared spectroscopy, low-energy electron diffraction, temperature-programmed desorption and first-principles density-functional theory. This combination of techniques has allowed us to accurately identify the molecular conformations present under different conditions, and discuss the overlayer structure in the context of the possible bonding footprints. We have observed coverage-dependent local symmetry breaking, with three-point bonded glycinate moieties forming an achiral arrangement at low coverages, and chirality developing with the presence of two-point bonded moieties at high coverages. Comparison with previous work on the self-assembly of simple amino acids on Cu{311} and the structurally-similar Cu{110} surface has allowed us to rationalise the different conditions necessary for the formation of ordered chiral overlayers.

Chiral-symmetry restoration in clustered hadronic matter

Chiral-symmetry restoration is usually discussed in the context of quark matter, a system of deconfined quarks. However, many systems like stable nuclei and neutron stars have quarks confined within nucleons. In the present paper we use a Fermi sea of three-quark clusters instead of a Fermi sea of deconfined quarks to investigate the in-medium quark condensate. We find that an enhancement of the chiral breaking in clustered matter as claimed in the literature is not a consequence of the clustering but rather dependent on the microscopic model dynamics.

Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Initial-condition problem for a chiral Gross-Neveu system

A time-dependent projection technique is used to treat the initial-value problem for self-interacting fermionic fields. On the basis of the general dynamics of the fields, we derive formal equations of kinetic-type for the set of one-body dynamical variables. A nonperturbative mean-field expansion can be written for these equations. We treat this expansion in lowest order, which corresponds to the Gaussian mean-field approximation, for a uniform system described by the chiral Gross-Neveu Hamiltonian. Standard stationary features of the model, such as dynamical mass generation due to chiral symmetry breaking and a phenomenon analogous to dimensional transmutation, are reobtained in this context. The mean-field time evolution of nonequilibrium initial states is discussed.

Quasi-homologous spherically symmetric branes and their symmetry breaking

We revisit the dynamical system-based approach of spherically symmetric vacuum braneworlds, pointing out and studying the existence of a transcritical bifurcation as the dark pressure parameter changes its sign, we analyze some consequences of not discard the brane cosmological constant. For instance, it is noteworthy that the existence of an isothermal state equation between the dark fluid parameters cannot be obtained via the requirement of a quasi-homologous symmetry of the vacuum. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.

Chiral transition of fundamental and adjoint quarks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical (super)symmetry vacuum properties of the supersymmetric Chern-Simons-matter model

By computing the two-loop effective potential of the D=3 N=1 supersymmetric Chern-Simons model minimally coupled to a massless self-interacting matter superfield, it is shown that supersymmetry is preserved, while the internal U(1) and the scale symmetries are broken at two-loop order, dynamically generating masses both for the gauge superfield and for the real component of the matter superfield.

Mirror symmetry breaking at the molecular level.

Reasoning from two basic principles of molecular physics, P invariance of electromagnetic interaction and the second law of thermodynamics, one would conclude that mirror symmetry retained in the world of chiral molecules. This inference is fully consistent with what is observed in inorganic nature. However, in the bioorganic world, the reverse is true. Mirror symmetry there is definitely broken. Is it possible to account for this phenomenon without going beyond conventional concepts of the kinetics of enantioselective processes? This study is an attempt to survey all existing hypotheses containing this phenomenon.

Spontaneous symmetry breaking in amnestically induced persistence

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of four phases, for this system: (i) classical nonpersistence, (ii) classical persistence, (iii) log-periodic nonpersistence, and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however, log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.

f t value of the 0(+)-> 0(+) beta(+) decay of (32)Ar: A measurement of isospin symmetry breaking in a superallowed decay

We determined the absolute branch of the T=2 superallowed decay of (32)Ar by detecting the beta(+)-delayed protons and gamma decays of the daughter state. We obtain b(SA)(beta)=(22.71 +/- 0.16)%, which represents the first determination of a proton branch to better than 1%. Using this branch along with the previously determined (32)Ar half-life and energy release, we determined ft=(1552 +/- 12) s for the superallowed decay. This ft value, together with the corrected Ft value extracted from previously known T=1 superallowed decays, yields a measurement of the isospin symmetry breaking correction in (32)Ar decay delta(exp)(C)=(2.1 +/- 0.8)%. This can be compared to a theoretical calculation delta(C)=(2.0 +/- 0.4)%. As by-products of this work, we determined the gamma and proton branches for the decay of the lowest T=2 state of (32)Cl, made a precise determination of the total proton branch and relative intensities of proton groups that leave (31)S in its first excited state and deduced an improved value for the (32)Cl mass.

Symmetry-breaking in cumulative measures of shapes of polymer models.

Using numerical simulations we investigate shapes of random equilateral open and closed chains, one of the simplest models of freely fluctuating polymers in a solution. We are interested in the 3D density distribution of the modeled polymers where the polymers have been aligned with respect to their three principal axes of inertia. This type of approach was pioneered by Theodorou and Suter in 1985. While individual configurations of the modeled polymers are almost always nonsymmetric, the approach of Theodorou and Suter results in cumulative shapes that are highly symmetric. By taking advantage of asymmetries within the individual configurations, we modify the procedure of aligning independent configurations in a way that shows their asymmetry. This approach reveals, for example, that the 3D density distribution for linear polymers has a bean shape predicted theoretically by Kuhn. The symmetry-breaking approach reveals complementary information to the traditional, symmetrical, 3D density distributions originally introduced by Theodorou and Suter.

Symmetry breaking in small rotating clouds of trapped ultracold Bose atoms

We study the signatures of rotational and phase symmetry breaking in small rotating clouds of trapped ultracold Bose atoms by looking at rigorously defined condensate wave function. Rotational symmetry breaking occurs in narrow frequency windows, where energy degeneracy between the lowest energy states of different total angular momentum takes place. This leads to a complex condensate wave function that exhibits vortices clearly seen as holes in the density, as well as characteristic local phase patterns, reflecting the appearance of vorticities. Phase symmetry (or gauge symmetry) breaking, on the other hand, is clearly manifested in the interference of two independent rotating clouds.

Critical Behavior and Axis Defining Symmetry Breaking in Hydra Embryonic Development

The formation of a hollow cellular sphere is often one of the first steps of multicellular embryonic development. In the case of Hydra, the sphere breaks its initial symmetry to form a foot-head axis. During this process a gene, ks1, is increasingly expressed in localized cell domains whose size distribution becomes scale-free at the axis-locking moment. We show that a physical model based solely on the production and exchange of ks1-promoting factors among neighboring cells robustly reproduces the scaling behavior as well as the experimentally observed spontaneous and temperature-directed symmetry breaking.

General method to determine replica symmetry breaking transitions

We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest lies in models where this symmetry is absent. We apply the method to long-range and short-range Ising spin-glasses with and without a magnetic field as well as short-range multispin interaction spin-glasses.