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At least 631 records · Page 35

Quantum–classical transition in the Caldeira–Leggett model

The quantum–classical transition in the Caldeira–Leggett model is investigated in the framework of the functional renormalization group method. It is shown that a divergent quadratic term arises in the action due to the heat bath in the model. By removing the divergence with a frequency cutoff we considered the critical behavior of the model. The critical exponents belonging to the susceptibility and the correlation length are determined and their independence of the frequency cutoff and the renormalization scheme is shown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Reexamination of the infrared properties of randomly stirred hydrodynamics

Dynamic renormalization-group (RG) methods were originally used by Forster, Nelson, and Stephen (FNS) to study the large-scale behavior of randomly stirred incompressible fluids governed by the Navier-Stokes equations. Similar calculations using a variety of methods have been performed but have led to a discrepancy in results. In this paper, we carefully reexamine in d dimensions the approaches used to calculate the renormalized viscosity increment and, by including an additional constraint which is neglected in many procedures, conclude that the original result of FNS is correct. By explicitly using step functions to control the domain of integration, we calculate a nonzero correction caused by boundary terms which cannot be ignored. We then go on to analyze how the noise renormalization, which is absent in many approaches, contributes an O(k{sup 2}) correction to the force autocorrelation and show conditions for this to be taken as a renormalization of the noise coefficient. Following this, we discuss the applicability of this RG procedure to the calculation of the inertial range properties of fluid turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exciton Hierarchies in Gapped Carbon Nanotubes

We present evidence that the strong electron-electron (e-e) interactions in gapped carbon nanotubes lead to finite hierarchies of excitons within a given nanotube subband. We study these hierarchies by employing a field theoretic reduction of the gapped carbon nanotube permitting e-e interactions to be treated exactly. We analyze this reduction by employing a Wilsonian-like numerical renormalization group. We are so able to determine the gap ratios of the one-photon excitons as a function of the effective strength of interactions. We also determine within the same subband the gaps of the two-photon excitons, the single particle gaps, as well as a subset of the dark excitons. The strong e-e interactions in addition lead to strongly renormalized dispersion relations where the consequences of spin-charge separation can be readily observed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Unmixing Symmetries

The low-lying spectra of atomic nuclei display diverse behaviors, for example, rotational bands, which can be described phenomenologically by simple symmetry groups such as spatial SU(3). This leads to the idea of dynamical symmetry, where the Hamiltonian commutes with the Casimir operator(s) of a group, and is block diagonal in subspaces defined by the group’s irreducible representations or irreps. Detailed microscopic calculations, however, show these symmetries are in fact often strongly mixed and the wave function fragmented across many irreps. More commonly, the fragmentation across members of a band are similar, which is called a quasidynamical symmetry. In this Letter I explicitly, albeit numerically, construct unitary transformations from a quasidynamical symmetry to a dynamical symmetry, adapting the similarity renormalization group (SRG) in order to transform away the symmetry-mixing parts of the Hamiltonian. In this work, the standard SRG produces unsatisfactory results, forcing the induced dynamical symmetry to be dominated by high-weight irreps irrespective of the original decomposition. Using spectral distribution theory to rederive and diagnose standard SRG, I introduce a new form of SRG. The new SRG transforms a quasidynamical symmetry to a dynamical symmetry, that is, unmixes the mixed symmetries, with intuitively more appealing results.

74 ATOMIC AND MOLECULAR PHYSICS↗

Misanthropic entropy and renormalization as a communication channel

A central physical question is the extent to which infrared (IR) observations are sufficient to reconstruct a candidate ultraviolet (UV) completion. We recast this question as a problem of communication, with messages encoded in field configurations of the UV being transmitted to the IR degrees of freedom via a noisy channel specified by renormalization group (RG) flow, with noise generated by coarse graining/decimation. We present an explicit formulation of these considerations in terms of lattice field theory, where we show that the “misanthropic entropy” — the mutual information obtained from decimating neighbors — encodes the extent to which information is lost in marginalizing over/tracing out UV degrees of freedom. Our considerations apply both to statistical field theories as well as density matrix renormalization of quantum systems, where in the quantum case, the statistical field theory analysis amounts to a leading-order approximation. As a concrete example, we focus on the case of the 2D Ising model, where we show that the misanthropic entropy detects the onset of the phase transition at the Ising model critical point.

Physics↗

Complexity functionals and complexity growth limits in continuous MERA circuits

Using the path integral associated to a cMERA tensor network, we provide an operational definition for the complexity of a cMERA circuit/state which is relevant to investigate the complexity of states in quantum field theory. In this framework, it is possible to explicitly establish the correspondence (Minimal) Complexity = (Least) Action. Remarkably, it is also shown how the cMERA complexity action functional can be seen as the action of a Liouville field theory, thus establishing a connection with two dimensional quantum gravity. Concretely, the Liouville mode is identified with the variational parameter defining the cMERA circuit. The rate of complexity growth along the cMERA renormalization group flow is obtained and shown to saturate limits which are in close resemblance to the fundamental bounds to the speed of evolution in unitary quantum dynamics, known as quantum speed limits. We also show that the complexity of a cMERA circuit measured through these complexity functionals, can be cast in terms of the variationally-optimized amount of left-right entanglement created along the cMERA renormalization flow. Our results suggest that the patterns of entanglement in states of a QFT could determine their dual gravitational descriptions through a principle of least complexity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

4 He+n+n continuum within an ab initio framework

In this study, the low-lying continuum spectrum of the 6 He nucleus is investigated for the first time within an ab initio framework that encompasses the 4 He+n+n three-cluster dynamics characterizing its lowest decay channel. This is achieved through an extension of the no-core shell model combined with the resonating-group method, in which energy-independent nonlocal interactions among three nuclear fragments can be calculated microscopically, starting from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with three-body scattering boundary conditions by means of the hyperspherical-harmonics method on a Lagrange mesh. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we find the known J π = 2 + resonance as well as a result consistent with a new low-lying second 2 + resonance recently observed at GANIL at ~2.6 MeV above the He6 ground state. We also find resonances in the 2 – , 1 + , and 0 – channels, while no low-lying resonances are present in the 0 + and 1 – channels.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbor interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain system for a wide range of spectral functions and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short-range interactions of the effective chain system permit these open-quantum systems to be efficiently simulated by the density matrix renormalization group methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Holography beyond conformal invariance and AdS isometry?

We suggest that the principle of holographic duality be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on its boundary, provided that the boundary operator represents the inverse propagators of the theory induced on the boundary by the Dirichlet boundary value problem in the bulk spacetime. This relation holds for operators of a general spin-tensor structure on generic manifolds with boundaries irrespective of their background geometry and conformal invariance, and it apparently underlies numerous O(N{sup 0}) tests of the AdS/CFT correspondence, based on direct calculation of the bulk and boundary partition functions, Casimir energies, and conformal anomalies. The generalized holographic duality is discussed within the concept of the “double-trace” deformation of the boundary theory, which is responsible in the case of large-N CFT coupled to the tower of higher-spin gauge fields for the renormalization group flow between infrared and ultraviolet fixed points. Potential extension of this method beyond the one-loop order is also briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Most Effective Model for Describing the Universal Behavior of a Noisy Kuramoto–Sivashinsky Equation as a Paradigmatic Model

We study a noisy Kuramoto–Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by scale-dependent parameters, is described by a Kardar–Parisi–Zhang (KPZ) equation. We consider this conjecture by analyzing a renormalization-group equation for a class of generalized KPZ equations. We then uniquely determine the parameter values of the KPZ equation that most effectively describes the universal long-wavelength behavior of the noisy KS equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Study of spin-polaron formation in 1D systems

We study numerically the formation of spin-polarons in low-dimensional systems. We consider a ferromagnetic Kondo lattice model with Hund coupling J{sub H} and localized spins interacting antiferromagnetically with coupling constant J. We investigate the ground state phase diagram as a function of the exchange couplings J{sub H} and J and as a function of the band filling, since it has been observed that doping either on the ferromagnetic or antiferromagnetic regime lead to formation of magnetic domains [1]. We explore the quasi-particle formation and phase separation using the density-matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Time-dependent coupled-cluster method for atomic nuclei

We study time-dependent coupled-cluster theory in the framework of nuclear physics. Based on Kvaal's bi-variational formulation of this method [S. Kvaal, arXiv:1201.5548], we explicitly demonstrate that observables that commute with the Hamiltonian are conserved under time evolution. We explore the role of the energy and of the similarity-transformed Hamiltonian under real and imaginary time evolution and relate the latter to similarity renormalization group transformations. Proof-of-principle computations of He-4 and O-16 in small model spaces, and computations of the Lipkin model illustrate the capabilities of the method

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Fate of superconductivity in three-dimensional disordered Luttinger semimetals

Superconducting instability can occur in three-dimensional quadratic band crossing semimetals only at a finite coupling strength due to the vanishing of density of states at the quadratic band touching point. Since realistic materials are always disordered to some extent, we study the effect of short-ranged-correlated disorder on this superconducting quantum critical point using a controlled loop-expansion applying dimensional regularization. The renormalization group (RG) scheme allows us to determine the RG flows of the various interaction strengths and shows that disorder destroys the superconducting quantum critical point. In fact, the system exhibits a runaway flow to strong disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Toward UV models of kinetic mixing and portal matter. VII. A light dark photon in the 3 𝑐 ⁢3 𝐿 ⁢1 𝐴 ⁢1 𝐵 model

The kinetic mixing (KM) portal, by which the Standard Model (SM) photon mixes with a light dark photon arising from a new 𝑈⁢(1) 𝐷 gauge group, allows for the possibility of viable scenarios of sub-GeV thermal dark matter with appropriately suppressed couplings to the SM. This KM can only occur if particles having both SM and dark quantum numbers, here termed portal matter, also exist. The presence of such types of states and the strong suggestion of a need to embed 𝑈⁢(1) 𝐷 into a non-Abelian gauge structure not too far above the TeV scale based on the renormalization-group equation running of the 𝑈⁢(1)𝐷 gauge coupling is potentially indicative of an enlarged group linking together the visible and dark sectors. The gauge group 𝐺 = 𝑆⁢𝑈⁢(3) 𝑐 × 𝑆⁢𝑈⁢(3) 𝐿 × 𝑈⁢(1) 𝐴 × 𝑈⁢(1) 𝐵 = 3 𝑐 ⁢3 𝐿 ⁢1 𝐴 ⁢1 𝐵 is perhaps the simplest setup wherein the SM and dark interactions are partially unified in a non-Abelian fashion that is not a simple product group of the form 𝐺 = 𝐺 SM × 𝐺 𝐷 encountered frequently in earlier work. The present paper describes the implications and phenomenology of this type of setup.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

125 GeV Higgs boson mass from 5D gauge-Higgs unification

In the context of a simple gauge-Higgs unification (GHU) scenario based on the gauge group SU( 3 )××U(1)" in a 5D flat space-time, we investigate the possibility of reproducing the observed Higgs boson mass of around 125 GeV. We introduce bulk fermion multiplets with a bulk mass and a (half-)periodic boundary condition. In our analysis, we adopt a low-energy effective theoretical approach of the GHU scenario, where the running Higgs quartic coupling is required to vanish at the compactification scale. Under this “gauge-Higgs condition,” we investigate the renormalization group evolution of the Higgs quartic coupling and find a relation between the bulk mass and the compactification scale so as to reproduce the 125 GeV Higgs boson mass. Through quantum corrections at the one-loop level, the bulk fermions contribute to the Higgs boson production and decay processes and deviate the Higgs boson signal strengths at the Large Hadron Collider experiments from the Standard Model (SM) predictions. Employing the current experimental data that show that the Higgs boson signal strengths for a variety of Higgs decay modes are consistent with the SM predictions, we obtain lower mass bounds on the lightest mode of the bulk fermions to be around 1 TeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗