Generic Choice Of Parameters Research Articles

Generalized Tonnetz and discrete Abel-Jacobi map

Motivated by classical Euler's {\em Tonnetz}, we introduce and study the combinatorics and topology of more general simplicial complexes Tonn$^{n,k}(L)$ of {\em Tonnetz type}. Out main result is that for a sufficiently generic choice of parameters the generalized tonnetz Tonn$^{n,k}(L)$ is a triangulation of a $(k-1)$-dimensional torus $T^{k-1}$. In the proof we construct and use the properties of a {\em discrete Abel-Jacobi map}, which takes values in the torus $T^{k-1} \cong \mathbb{R}^{k-1}/\Lambda$ where $\Lambda \cong \mathbb{A}^\ast_{k-1}$ is the permutohedral lattice.

On the integrability of Hamiltonian 1:2:2 resonance

We study the integrability of the Hamiltonian normal form of 1:2:2 resonance. It is known that this normal form truncated to order three is integrable. The truncated to order four normal form contains many parameters. For a generic choice of parameters in the normal form up to order four, we carry on non-integrability analysis, based on the Morales–Ramis theory using only first variational equations along certain particular solutions. The non-integrability obtained by algebraic proofs produces dynamics illustrated by some numerical experiments.We also isolate a non-trivial case of integrability.

From 6d flows to 4d flows

SCFTs in six dimensions are interrelated by networks of RG flows. Compactifying such models on a Riemann surface with flux for the 6d global symmetry, one can obtain a wide variety of theories in four dimensions. These four dimensional models are also related by a network of RG flows. In this paper we study some examples of four dimensional flows relating theories that can be obtained from six dimensions starting with different SCFTs connected by 6d RG flows. We compile a dictionary between different orders of such flows, 6d → 6d → 4d and 6d → 4d → 4d, in the particular case when the six dimensional models are the ones residing on M5 branes probing different A-type singularities. The flows we study are triggered by vacuum expectation values (vevs) to certain operators charged under the six dimensional symmetry. We find that for generic choices of parameters the different orders of flows, 6d → 6d → 4d and 6d → 4d → 4d, involve compactifications on different Riemann surfaces with the difference being in the number of punctures the surface has.

Ghostfree quadratic curvature theories with massive spin-2 and spin-0 particles

We consider generic derivative corrections to the Einstein gravity and find new classes of theories without ghost around the Minkowski background by means of an extension of the spacetime geometry. We assume the Riemann-Cartan geometry, i.e., a geometry with a nonvanishing torsion, and consider all possible terms in the Lagrangian up to scaling dimension four. We first clarify the number, spins, and parities of all particle species around the Minkowski background and find that some of those particle species are ghosts for generic choices of parameters. For special choices of the parameters, on the other hand, those would-be ghosts become infinitely heavy and thus can be removed from the physical content of particle species. Imposing the conditions on the coupling constants to eliminate the ghosts, we find new quadratic curvature theories which are ghostfree around the Minkowski background for a range of parameters. A key feature of these theories is that there exist a nonghost massive spin-2 particle and a nonghost massive spin-0 particle in the graviton propagator, as well as the massless spin-2 graviton. In the limit of the infinite mass of the torsion, the Riemann-Cartan geometry reduces to the Riemannian geometry and thus the physical content of particle species coincides with that of the well-known quadratic curvature theory in the metric formalism, i.e., a massive spin-2 ghost, a massive spin-0 particle and the massless spin-2 graviton. Ghostfreedom therefore sets, besides other constraints, an upper bound on the mass of the torsion. In addition to the above mentioned particle species (a massive spin-2 particle, a massive spin-0 particle and the massless spin-2 graviton), the ghostfree theory contains either the set of a massive spin-1 and a massive spin-0 (Class I) or a couple of spin-1 (Class II). These additional particle species mediate gravity sourced by the spin of matter fields.

Why concave rather than convex inflaton potential?

The Planck data on cosmic microwave background indicates that the Starobinsky-type model with concave inflation potential is favored over the convex-type chaotic inflation. Is there any reason for that? Here we argue that if our universe began with a Euclidean wormhole, then the Starobinsky-type inflation is probabilistically favored. It is known that for a more generic choice of parameters than that originally assumed by Hartle and Hawking, the Hartle–Hawking wave function is dominated by Euclidean wormholes, which can be interpreted as the creation of two classical universes from nothing. We show that only one end of the wormhole can be classicalized for a convex potential, while both ends can be classicalized for a concave potential. The latter is therefore more probable.

A compact minimal space Y such that its square Y × Y is not minimal

The following well known open problem is answered in the negative: Given two compact spaces X and Y that admit minimal homeomorphisms, must the Cartesian product X×Y admit a minimal homeomorphism as well? Moreover, it is shown that such spaces can be realized as minimal sets of torus homeomorphisms homotopic to the identity. A key element of our construction is an inverse limit approach inspired by combination of a technique of Aarts & Oversteegen and the construction of Slovak spaces by Downarowicz & Snoha & Tywoniuk. This approach allows us also to prove the following result. Let ϕ:M×R→M be a continuous, aperiodic minimal flow on the compact, finite-dimensional metric space M. Then there is a generic choice of parameters c∈R, such that the homeomorphism h(x)=ϕ(x,c) admits a noninvertible minimal map f:M→M as an almost 1-1 extension.

Miscible–immiscible transition and nonequilibrium scaling in two-component driven open condensate wires

We investigate the steady state phase diagram of two-component driven open condensates (DOCs) in one dimension. We identify a miscible–immiscible transition which is predominantly driven by gapped density fluctuations and occurs upon increasing the inter-component dissipative coupling. Below the transition in the miscible phase, we find the effective long wavelength dynamics to be described by a two-component Kardar–Parisi–Zhang (KPZ) equation that belongs to the nonequilibrium universality class of the one-dimensional single-component KPZ equation at generic choices of parameters. Our results are relevant for different experimental realizations for two-component DOCs in exciton–polariton systems.

Faking ordinary photons by displaced dark photon decays

A light meta-stable dark photon decaying into collimated electron/positron pair can fake a photon, either converted or unconverted, at the LHC. The detailed object identification relies on the specifics of the detector and strategies for the reconstruction. We study the fake rate based on the ATLAS(CMS) detector geometry and show that it can be O(1) with a generic choice of parameters. Especially, the probability of being registered as a photon is angular dependent. Such detector effects can induce bias to measurements on certain properties of new physics. In this paper, we consider the scenario where dark photons in final states are from a heavy resonance decay. Consequently, the detector effects can dramatically affect the results when determine the spin of a resonance. Further, if the decay products from the heavy resonance are one photon and one dark photon, which has a large probability to fake a diphoton event, the resonance is allowed to be a vector. Due to the difference in detector, the cross sections measured in ATLAS and CMS do not necessarily match. Furthermore, if the diphoton signal is given by the dark photons, the SM $Z\gamma$ and $ZZ$ final states do not necessarily come with the $\gamma\gamma$ channel, which is a unique signature in our scenario. The issue studied here is relevant also for any future new physics searches with photon(s) in the final state. We discuss possible ways of distinguishing dark photon decay and real photon in the future.

Deformation Theory of Periodic Monopoles (With Singularities)

We show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities), i.e. monopoles on $\mathbb{R}^{2} \times \mathbb{S}^{1}$ possibly singular at a finite collection of points, are either empty or smooth hyperk\"ahler manifolds. Furthermore, we prove an index theorem and therefore compute the dimension of the moduli spaces.

The core control system of intracellular iron homeostasis: A mathematical model

Iron is a metal essential for cellular metabolism. However, excess iron available for reactions contributes to the formation of dangerous reactive oxygen species, such as the hydroxyl radical, via the Fenton reaction. Therefore, intracellular iron levels are tightly constrained by a control system of proteins. This paper contains a mathematical model, in the form of a system of five ordinary differential equations, of the core of this control system, including the labile iron pool as well as proteins that regulate uptake, storage, and export and are connected through negative feedback loops. The model is validated using data from an overexpression experiment with cultured human breast epithelial cells. The parameters in the mathematical model are not known for this particular cell culture system, so the analysis of the model was done for a generic choice of parameters. Through a mixture of analytical arguments and extensive simulations it is shown that for any choice of parameters the model reaches a unique stable steady state, thereby ruling out oscillatory behavior. It is shown furthermore that the model parameters are identifiable through suitable experiments.

On the new massive gravity and AdS/CFT

Demanding the existence of a simple holographic c-theorem, it is shown that a general (parity preserving) theory of gravity in 2+1 dimensions involving upto four derivative curvature invariants reduces to the new massive gravity theory. We consider extending the theory including upto six derivative curvature invariants. Black hole solutions are presented and consistency with 1+1 CFTs is checked. We present evidence that bulk unitarity is still in conflict with a positive CFT central charge for generic choice of parameters.

Interaction correction of conductivity near a ferromagnetic quantum critical point

We calculate the temperature dependence of conductivity due to interaction correction for a disordered itinerant electron system close to a ferromagnetic quantum critical point, which occurs due to a spin-density wave instability. In the quantum critical regime, the crossover between diffusive and ballistic transport occurs at a temperature T* = 1/[{tau}{gamma}(e{sub F}{tau}){sup 2}], where {gamma} is the parameter associated with the Landau damping of the spin fluctuations, {tau} is the impurity scattering time, and E{sub F} is the Fermi energy. For a generic choice of parameters, T* is a few orders of magnitude smaller than the usual crossover scale 1/{tau}. In the ballistic quantum critical regime, the conductivity has a T{sup (d-1)/3} temperature dependence where d is the dimensionality of the system. In the diffusive quantum critical regime, we get T{sup 1/4} dependence in three dimensions and In{sup 2} T dependence in two dimensions. Away from the quantum critical regime, we recover the standard results for a good metal.

Quantum Correction to Conductivity Close to a Ferromagnetic Quantum Critical Point in Two Dimensions

We study the temperature dependence of the conductivity due to quantum interference processes for a two-dimensional disordered itinerant electron system close to a ferromagnetic quantum critical point. Near the quantum critical point, the crossover between diffusive and ballistic regimes of quantum interference effects occurs at a temperature T*=1/taugamma(E(F)tau)2, where gamma is the parameter associated with the Landau damping of the spin fluctuations, tau is the impurity scattering time, and E(F) is the Fermi energy. For a generic choice of parameters, T* is smaller than the nominal crossover scale 1/tau. In the ballistic quantum critical regime, the conductivity behaves as T1/3.

A semi-classical study of the Casati–Prosen triangle map

We investigate the semi-classical properties of a two-parameter family of piece-wise linear maps on the torus known as the Casati–Prosen or triangle map. This map is weakly chaotic and has zero Lyapunov exponent. A correspondence between classical and quantum observables is established, leading to an appropriate statement regarding equidistribution of eigenfunctions in the semi-classical limit. We then give a full description of our numerical study of the eigenvalues and eigenvectors of this family of maps. For generic choices of parameters, the spectral and eigenfunction statistics are seen to follow the predictions of the random matrix theory conjecture.

Classical and quantum initial value problems for models of chronology violation.

We study the classical and quantum theory of a class of nonlinear differential equations on chronology violating spacetime models in which space consists of finitely many discrete points. Classically, in the linear and weakly nonlinear regimes (for generic choices of parameters) we prove existence and uniqueness of solutions corresponding to initial data specified before the dischronal region; however, uniqueness (but not existence) fails in the strongly coupled regime. The evolution preserves the symplectic structure. The quantum theory is approached via the quantum initial value problem (QIVP); that is, by seeking operator-valued solutions to the equation of motion with initial data representing the canonical (anti)commutation relations. Using normal operator ordering, we construct solutions to the QIVP for both Bose and Fermi statistics (again for generic choice of parameters) and prove that these solutions are unique. For models with two spatial points, the resulting evolution is unitary; however, for a more general model the evolution fails to preserve the (anti)commutation relations and is therefore nonunitary. We show that this nonunitary evolution cannot be described using a superscattering operator with the usual properties. We present numerical evidence to show that the bosonic quantum theory can pick out a unique classical limit for certain ranges of the coupling strength, even when there are many classical solutions. We show that the quantum theory depends strongly on the choice of operator ordering. In addition, we show that our results differ from those obtained using the ``self-consistent path integral''. It follows that the path integral evolution does not correspond to a solution of the equation of motion.