Non-trivial Profile Research Articles

Chebyshev Polynomials in the Physics of the One-Dimensional Finite-Size Ising Model: An Alternative View and Some New Results

For studying the finite-size behavior of the Ising model under different boundary conditions, we propose an alternative to the standard transfer matrix technique approach based on Abelès theorem and Chebyshev polynomials. Using it, one can easily reproduce the known results for periodic boundary conditions concerning the Lee–Yang zeros, the exact position-space renormalization-group transformation, etc., and can extend them by deriving new results for antiperiodic boundary conditions. Note that in the latter case, one has a nontrivial order parameter profile, which we also calculate, where the average value of a given spin depends on the distance from the seam with the opposite bond in the system. It is interesting to note that under both boundary conditions, the one-dimensional case exhibits Schottky anomaly.

Optical vortex ladder via Sisyphus pumping of Pseudospin

Robust high-order optical vortices are much in demand for applications in optical manipulation, optical communications, quantum entanglement and quantum computing. However, in numerous experimental settings, a controlled generation of optical vortices with arbitrary orbital angular momentum remains a challenge. Here, we present a concept of “optical vortex ladder” for the stepwise generation of optical vortices through Sisyphus pumping of pseudospin modes in photonic graphene. The ladder is applicable in various lattices with Dirac-like structures. Instead of conical diffraction and incomplete pseudospin conversion under conventional Gaussian beam excitations, the vortices produced in the ladder arise from non-trivial topology and feature diffraction-free Bessel profiles, thanks to the refined excitation of the ring spectrum around the Dirac cones. By employing a periodic “kick” to the photonic graphene, effectively inducing the Sisyphus pumping, the ladder enables tunable generation of optical vortices of any order even when the initial excitation does not involve any orbital angular momentum. The optical vortex ladder stands out as an intriguing non-Hermitian dynamical system, and, among other possibilities, opens a pathway for applications of topological singularities in beam shaping and wavefront engineering.

Anomalous dimension and quasinormal modes of flavor branes

We study scalar quasinormal modes in a D3/D7 system holographically dual to a quantum field theory with chiral symmetry breaking at finite temperature. From the bottom-up approach, we consider a nontrivial dilaton profile which is responsible for the anomalous dimension of the quark condensate. It depends on a new parameter q in the model. By varying this parameter, we study the behavior of the massive and massless scalar quasinormal modes. The numerical method that we use is the spectral method, and we find that there is no pure imaginary mode for the massless case but it appears by increasing the parameter q. It is known that this mode becomes tachyonic for massive cases. Then we turn on a pseudoscalar field and using a simple ansatz study its effect on the quasinormal modes of the scalar field. By varying the parameter of the nontrivial dilaton profile in the model, we qualitatively study quasinormal modes in walking theories.

Liouville gravity at the end of the world:deformed defects in AdS/BCFT

We study shape deformations of two-dimensional end-of-the-world (ETW) branes, such as those in bottom-up models of two-dimensional holographic boundary conformal field theories (BCFT), and derive an action for the theory of brane deformations in any bulk three-dimensional maximally symmetric spacetime. In the case of a bulk anti-de Sitter (AdS) spacetime, at leading order in the ultraviolet cutoff, the induced theory on the brane controlling its shape is Liouville gravity coupled to quantum matter. We show in certain limits the theory reduces to semi-classical AdS, dS or flat Jackiw-Teitelboim (JT) gravity, thus providing the first doubly-holographic derivation of two-dimensional models of dilaton gravity minimally coupled to a large number of conformal fields. Specializing to the AdS JT gravity limit, we discuss the dual BCFT interpretation and provide evidence that changing the boundary conditions of JT gravity on the brane is equivalent to a deformation of the dual BCFT with the displacement operator. This establishes a doubly-holographic triality between (i) brane deformations in the bulk, (ii) JT gravity in the brane description, and (iii) irrelevant deformations of the CFT boundary. Lastly, in the presence of a non-trivial dilaton profile, we prove that the Ryu-Takayanagi formula for holographic BCFTs receives a contact term whenever the minimal surface ends on the brane.

Energy-momentum tensor of the dilute (3+1)D glasma

We present a succinct formulation of the energy-momentum tensor of the glasma characterizing the initial color fields in relativistic heavy-ion collisions in the color glass condensate effective theory. We derive concise expressions for the (3+1)D dynamical evolution of symmetric nuclear collisions in the weak field approximation employing a generalized McLerran-Venugopalan model with nontrivial longitudinal correlations. Utilizing Monte Carlo integration, we calculate in unprecedented detail non-trivial rapidity profiles of early time observables at RHIC and LHC energies, including transverse energy densities and eccentricities. For our setup with broken boost invariance, we carefully discuss the placement of the origin of the Milne frame and interpret the components of the energy-momentum tensor. We find longitudinal flow that deviates from standard Bjorken flow in the (3+1)D case and provide a geometric interpretation of this effect. Furthermore, we observe a universal shape in the flanks of the rapidity profiles regardless of collision energy and predict that limiting fragmentation should also hold at LHC energies. Published by the American Physical Society 2024

A worldsheet description of flux compactifications

We demonstrate how recent developments in string field theory provide a framework to systematically study type II flux compactifications with non-trivial Ramond-Ramond profiles. We present an explicit example where physical observables can be computed order by order in a small parameter which can be effectively viewed as string coupling constant. We obtain the corresponding background solution of the string field equations of motions up to the second order in the expansion. Along the way, we show how the tadpole cancellations of the string field equations lead to the minimization of the F-term potential of the low energy supergravity description. String field action expanded around the obtained background solution furnishes a “worldsheet” description of the flux compactifications.

Compact objects in and beyond the standard model from nonperturbative vacuum scalarization

We consider a theory in which a real scalar field is Yukawa coupled to a fermion and has a potential with two nondegenerate vacua. If the coupling is sufficiently strong, a collection of N fermions deforms the true vacuum state, creating energetically favored false-vacuum pockets in which fermions are trapped. We embed this model within general relativity and prove that it admits self-gravitating compact objects where the scalar field acquires a nontrivial profile due to nonperturbative effects. We discuss some applications of this general mechanism: (i) “neutron soliton stars” in low-energy effective QCD, which naturally happen to have masses around 2M⊙ and radii around 10 km even without neutron interactions; (ii) “Higgs false-vacuum pockets” in and beyond the standard model; (iii) “dark soliton stars” in models with a dark sector. In the latter two examples, we find compelling solutions naturally describing centimeter-size compact objects with masses around 10−6M⊙, intriguingly in a range compatible with the Optical Gravitational Lensing Experiment (OGLE)+Hyper Suprime-Cam (HSC) microlensing anomaly. In addition to these interesting examples, the mechanism of nonperturbative vacuum scalarization may play a role in various contexts in and beyond the standard model, providing a support mechanism for new compact objects that can form in the early Universe, can collapse into primordial black holes through accretion past their maximum mass, and serve as dark matter candidates. Published by the American Physical Society 2024

Single‐Mode Electrically Pumped Terahertz Laser in an Ultracompact Cavity via Merging Bound States in the Continuum

AbstractPhotonic bound states in the continuum (BICs) are highly localized optical modes that have found important applications in lasers, sensors, modulators, and harmonic signal generators. While possessing a higher quality factor (Q) as compared to leaky photonic modes, regular BICs (e.g., either symmetry‐protected or accidental BICs) normally require large cavity sizes and are usually sensitive to the fabrication imperfections that introduce lattice disorders. Moreover, the previous demonstrations of BIC lasers are mostly based on optical pumping and operated in the visible and near‐infrared regimes. Here, an electrically pumped BIC laser is demonstrated by merging two types of BIC modes based on a quantum cascade chip in the terahertz (THz) regime, which has an ultra‐compact size (with a pump area around 4λ2). The measured side‐mode suppression ratio (SMSR) can reach up to ≈20 dB, indicating a good single‐mode performance over the entire dynamic range. In addition, the emitted beam shows a nontrivial cylindrical vector beam profile, a typical topological feature of BIC lasers. This work would pave the way for practical use of the emerging BIC concepts in pursuing ultra‐compact and high‐performance electrically driven laser sources, which are highly desired in advanced optoelectronics and integrated photonics.

Symmetric exclusion process under stochastic power-law resetting

We study the behaviour of a symmetric exclusion process in the presence of non-Markovian stochastic resetting, where the configuration of the system is reset to a step-like profile at power-law waiting times with an exponent α. We find that the power-law resetting leads to a rich behaviour for the currents, as well as density profile. We show that, for any finite system, for α < 1, the density profile eventually becomes uniform while for α > 1, an eventual non-trivial stationary profile is reached. We also find that, in the limit of thermodynamic system size, at late times, the average diffusive current grows with for , for and θ = 1 for α > 1. We also analytically characterize the distribution of the diffusive current in the short-time regime using a trajectory-based perturbative approach. Using numerical simulations, we show that in the long-time regime, the diffusive current distribution follows a scaling form with an dependent scaling function. We also characterise the behaviour of the total current using renewal approach. We find that the average total current also grows algebraically where for , for , while for the average total current reaches a stationary value, which we compute exactly. The standard deviation of the total current also shows an algebraic growth with an exponent for , and for , whereas it approaches a constant value for α > 2. The total current distribution remains non-stationary for α < 1, while, for α > 1, it reaches a non-trivial and strongly non-Gaussian stationary distribution, which we also compute using the renewal approach.

Breathers and rogue waves for semilinear curl-curl wave equations

We consider localized solutions of variants of the semilinear curl-curl wave equation s(x) partial _t^2 U +nabla times nabla times U + q(x) U pm V(x) vert U vert ^{p-1} U = 0 for (x,t)in {mathbb {R}}^3times {mathbb {R}} and arbitrary p>1. Depending on the coefficients s, q, V we can prove the existence of three types of localized solutions: time-periodic solutions decaying to 0 at spatial infinity, time-periodic solutions tending to a nontrivial profile at spatial infinity (both types are called breathers), and rogue waves which converge to 0 both at spatial and temporal infinity. Our solutions are weak solutions and take the form of gradient fields. Thus they belong to the kernel of the curl-operator so that due to the structural assumptions on the coefficients the semilinear wave equation is reduced to an ODE. Since the space dependence in the ODE is just a parametric dependence we can analyze the ODE by phase plane techniques and thus establish the existence of the localized waves described above. Noteworthy side effects of our analysis are the existence of compact support breathers and the fact that one localized wave solution U(x, t) already generates a full continuum of phase-shifted solutions U(x,t+b(x)) where the continuous function b:{mathbb {R}}^3rightarrow {mathbb {R}} belongs to a suitable admissible family.

Photocleavable Anionic Glues for Light-Responsive Nanoparticle Aggregates.

Integrating light-sensitive molecules within nanoparticle (NP) assemblies is an attractive approach to fabricate new photoresponsive nanomaterials. Here, we describe the concept of photocleavable anionic glue (PAG): small trianions capable of mediating interactions between (and inducing the aggregation of) cationic NPs by means of electrostatic interactions. Exposure to light converts PAGs into dianionic products incapable of maintaining the NPs in an assembled state, resulting in light-triggered disassembly of NP aggregates. To demonstrate the proof-of-concept, we work with an organic PAG incorporating the UV-cleavable o-nitrobenzyl moiety and an inorganic PAG, the photosensitive trioxalatocobaltate(III) complex, which absorbs light across the entire visible spectrum. Both PAGs were used to prepare either amorphous NP assemblies or regular superlattices with a long-range NP order. These NP aggregates disassembled rapidly upon light exposure for a specific time, which could be tuned by the incident light wavelength or the amount of PAG used. Selective excitation of the inorganic PAG in a system combining the two PAGs results in a photodecomposition product that deactivates the organic PAG, enabling nontrivial disassembly profiles under a single type of external stimulus.

Photonic Majorana quantum cascade laser with polarization-winding emission

Topological cavities, whose modes are protected against perturbations, are promising candidates for novel semiconductor laser devices. To date, there have been several demonstrations of topological lasers (TLs) exhibiting robust lasing modes. The possibility of achieving nontrivial beam profiles in TLs has recently been explored in the form of vortex wavefront emissions enabled by a structured optical pump or strong magnetic field, which are inconvenient for device applications. Electrically pumped TLs, by contrast, have attracted attention for their compact footprint and easy on-chip integration with photonic circuits. Here, we experimentally demonstrate an electrically pumped TL based on photonic analogue of a Majorana zero mode (MZM), implemented monolithically on a quantum cascade chip. We show that the MZM emits a cylindrical vector (CV) beam, with a topologically nontrivial polarization profile from a terahertz (THz) semiconductor laser.

Asymptotic stability of rarefaction wave for a blood flow model

This paper is concerned with nonlinear stability of rarefaction wave to the Cauchy problem for a blood flow model, which describes the motion of blood through axi‐symmetric compliant vessels. Inspired by the stability analysis of classical ‐system, we show the solution of this typical model tends time‐asymptotically toward the rarefaction wave under some suitably small conditions and there are more difficulties in the proof due to the appearance of strong nonlinear terms regarding second‐order derivative of with respect to the spatial variable . The main result is proved by employing the elementary energy methods. This is the first result regarding nonlinear stability of some nontrivial profiles (i.e., non‐constant function patterns) for the blood flow model.

Formation of hot spots around small primordial black holes

In this paper, we investigate the thermalization of Hawking radiation from primordial black holes (PBHs) in the early Universe, taking into account the interference effect on thermalization of high energy particles, known as Landau-Pomeranchuk-Migdal (LPM) effect. Small PBHs with masses ≲ 109 g completely evaporate before the big bang nucleosynthesis (BBN). The Hawking radiation emitted from these PBHs heats up the ambient plasma with temperature lower than the Hawking temperature, which results in a non-trivial temperature profile around the PBHs, namely a hot spot surrounding a PBH with a broken power-law tail. We find that the hot spot has a core with a radius much larger than the black hole horizon and its highest temperature is independent of the initial mass of the PBH such as 2 × 109 GeV × (α/0.1)19/3, where α generically represents the fine-structure constants. We also briefly discuss the implications of the existence of the hot spot for phenomenology.

Magnetic response of a two-dimensional viscous electron fluid

It has been established that the Coulomb interactions can transform the electron gas into a viscous fluid. This fluid is realized in a number of platforms, including graphene and two-dimensional semiconductor heterostructures. The defining characteristic of the electron fluid is the formation of layers of charge carriers that are in local thermodynamic equilibrium, as in classical fluids. In the presence of nonuniformities, whirlpools and nontrivial flow profiles are formed, which have been directly imaged in recent experiments. In this paper, we theoretically study the response of the electron fluid to localized magnetic fields. We find that the electric current is suppressed by viscous vortices in regions where magnetic field is sharply varying, causing strong transport signatures. Experimentally, our considerations are relevant since local magnetic fields can be applied to the system through implanting adatoms or embedding micromagnets in the top-gate. Our theory is essential for the characterization and future applications of electron fluids in hydrodynamic spin transport.

Calculation of Interrelated Thermal Processes in a Submersible Electric Motor, Rocks and Water-Gas-Oil Flow in a Producing Well

This paper is devoted to the study of interrelated thermal processes in a submersible electric motor of a pumping unit located in an oil-producing well and flowed around by a water-oil-gas reservoir mixture, taking into account the heat exchange of the flow with the rocks surrounding the well. To describe these processes, mathematical and numerical models are developed. The numerical model and algorithms are implemented in a software that allows to study temperature fields and various thermal effects using computational experiments with simultaneous visualization of the results of computations. It is shown, in particular, that the transient thermal processes in the system “motor — three-phase flow – rocks”, when the motor is turned off due to its heating to the maximum permissible temperature depend on the physical and geometrical characteristics of each element of the system and are characterized by a non-trivial temperature profiles in rocks. Calculated estimates of the duration (on the order of tens of minutes) of the cooling stage of the motor after it is turned off and its heating stage when it is turned on again correspond to the real times of these processes in producing oil wells.

Factorizing wormholes in a partially disorder-averaged SYK model

In this paper, we introduce a “partially disorder-averaged” SYK model. This model has a real parameter that smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large N effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields. These local fields can be understood as “half” of the bi-local collective fields, and in the totally fixed-coupling limit, they represent the “half-wormholes” which were found in recent studies. We find that the large N saddles of these local fields vanish in the total-disorder-averaged limit, while they develop nontrivial profiles as we gradually fix the coupling constants. We argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic AdS boundary. This illuminates how the half-wormhole saddles emerge in the SYK model with fixed couplings.

Stability of neutron stars in Horndeski theories with Gauss-Bonnet couplings

In Horndeski theories containing a scalar coupling with the Gauss-Bonnet (GB) curvature invariant ${R}_{\mathrm{GB}}^{2}$, we study the existence and linear stability of neutron star (NS) solutions on a static and spherically symmetric background. For a scalar-GB coupling of the form $\ensuremath{\alpha}\ensuremath{\xi}(\ensuremath{\phi}){R}_{\mathrm{GB}}^{2}$, where $\ensuremath{\xi}$ is a function of the scalar field $\ensuremath{\phi}$, the existence of linearly stable stars with a nontrivial scalar profile without instabilities puts an upper bound on the strength of the dimensionless coupling constant $|\ensuremath{\alpha}|$. To realize maximum masses of NSs for a linear (or dilatonic) GB coupling ${\ensuremath{\alpha}}_{\mathrm{GB}}\ensuremath{\phi}{R}_{\mathrm{GB}}^{2}$ with typical nuclear equations of state, we obtain the theoretical upper limit $\sqrt{|{\ensuremath{\alpha}}_{\mathrm{GB}}|}&lt;0.7\text{ }\text{ }\mathrm{km}$. This is tighter than those obtained by the observations of gravitational waves emitted from binaries containing NSs. We also incorporate cubic-order scalar derivative interactions, quartic derivative couplings with nonminimal couplings to a Ricci scalar besides the scalar-GB coupling, and show that NS solutions with a nontrivial scalar profile satisfying all the linear stability conditions are present for certain ranges of the coupling constants. In regularized four-dimensional Einstein-GB gravity obtained from a Kaluza-Klein reduction with an appropriate rescaling of the GB coupling constant, we find that NSs in this theory suffer from a strong coupling problem as well as Laplacian instability of even-parity perturbations. We also study NS solutions with a nontrivial scalar profile in power-law $F({R}_{\mathrm{GB}}^{2})$ models, and show that they are pathological in the interior of stars and plagued by ghost instability together with the asymptotic strong coupling problem in the exterior of stars.

Exact scalar (quasi-)normal modes of black holes and solitons in gauged SUGRA

In this paper we identify a new family of black holes and solitons that lead to the exact integration of scalar probes, even in the presence of a non-minimal coupling with the Ricci scalar which has a non-trivial profile. The backgrounds are planar and spherical black holes as well as solitons of SU (2) × SU (2) mathcal{N} = 4 gauged supergravity in four dimensions. On these geometries, we compute the spectrum of (quasi-)normal modes for the non-minimally coupled scalar field. We find that the equation for the radial dependence can be integrated in terms of hypergeometric functions leading to an exact expression for the frequencies. The solutions do not asymptote to a constant curvature spacetime, nevertheless the asymptotic region acquires an extra conformal Killing vector. For the black hole, the scalar probe is purely ingoing at the horizon, and requiring that the solutions lead to an extremum of the action principle we impose a Dirichlet boundary condition at infinity. Surprisingly, the quasinormal modes do not depend on the radius of the black hole, therefore this family of geometries can be interpreted as isospectral in what regards to the wave operator non-minimally coupled to the Ricci scalar. We find both purely damped modes, as well as exponentially growing unstable modes depending on the values of the non-minimal coupling parameter. For the solitons we show that the same integrability property is achieved separately in a non-supersymmetric solutions as well as for the supersymmetric one. Imposing regularity at the origin and a well defined extremum for the action principle we obtain the spectra that can also lead to purely oscillatory modes as well as to unstable scalar probes, depending on the values of the non-minimal coupling.

Blow-up of waves on singular spacetimes with generic spatial metrics

We study the asymptotic behaviour of solutions to the linear wave equation on cosmological spacetimes with Big Bang singularities and show that appropriately rescaled waves converge against a blow-up profile. Our class of spacetimes includes Friedman–Lemaître–Robertson–Walker (FLRW) spacetimes with negative sectional curvature that solve the Einstein equations in the presence of a perfect irrotational fluid with p=(gamma -1)rho . As such, these results are closely related to the still open problem of past nonlinear stability of such FLRW spacetimes within the Einstein scalar field equations. In contrast to earlier works, our results hold for spatial metrics of arbitrary geometry, hence indicating that the matter blow-up in the aforementioned problem is not dependent on spatial geometry. Additionally, we use the energy estimates derived in the proof in order to formulate open conditions on the initial data that ensure a non-trivial blow-up profile, for initial data sufficiently close to the Big Bang singularity and with less harsh assumptions for gamma <2.