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A higher-order nonlinear Boussinesq system with a time-dependent boundary delay is considered. Sufficient conditions are presented to ensure the well-posedness of the problem, utilizing Kato's variable norm technique and the Fixed-Point Theorem. More significantly, the energy decay for the linearized problem is demonstrated using the energy method., Comment: 17 pages. Comments are welcome

We present a systematic study of the energy levels of twisted bilayer graphene (tBLG) quantum dots (QD) and rings (QR) under an external perpendicular magnetic field. The confinement structures are modeled by a circular dot-like- and ring-like-shaped site-dependent staggered potential, which prevents edge effects and leads to an energy gap between the electron and hole states. Results are obtained within the tight-binding model with interlayer hopping parameters defined by the Slater-Koster form for different interlayer twist angles $\theta$. Our findings show that, for $\theta$ around 0$^\circ$ or $60^\circ$, the energy spectra exhibit features resulting from the interplay between characteristics of the AA and AB/BA stacking orders that compose the moir\'e pattern of such tBLG, while the low-energy levels are shown to be nearly independent on the rotation angle for $10^\circ\lesssim \theta\lesssim 50^\circ$. In the absence of a magnetic field, the energy levels of the QR scale with its width $W$ according to a power law $W^{-\alpha}$, whose exponent $1 \lessapprox\alpha\lessapprox 2$ depends on the twist angle. Most interestingly, the lowest energy states of tBLG QRs oscillate as a function of its average radius, with the oscillation period matching half of the moir\'e period. In the presence of an intense magnetic field, the lowest energy levels for the tBLG QDs and QRs match almost perfectly, regardless of whether the external radius of the quantum confinement structure is smaller or on the order of the moir\'e period, which is due to the interplay of the trigonal warping effect and the preferential localization of the eigenstates. Our results reveal relevant information about the moir\'e pattern in tBLG and its role in charge particle confinement., Comment: 16 pages, 12 figures

This work establishes a series of no-go conjectures that impose rigorous constraints on the localization of bulk fields in braneworld scenarios, specifically affecting gauge and spinor fields within five-dimensional spacetimes. Our approach differs from traditional methods as it does not rely on specific equations of motion, making our results broadly applicable across various braneworld models. These no-go conditions reveal fundamental limitations in field localization, challenging the feasibility of embedding fields on the brane. For instance, our analysis demonstrates that existing models fail to achieve consistent localization for gauge and spinor fields. Additionally, one of our conditions indicates that the effective Lagrangian on the brane cannot exhibit conformal invariance.

The basal plane of graphene can function as a selective barrier that is permeable to protons but impermeable to all ions and gases, stimulating its use in applications such as membranes, catalysis and isotope separation. Protons can chemically adsorb on graphene and hydrogenate it, inducing a conductor-insulator transition that has been explored intensively in graphene electronic devices. However, both processes face energy barriers and various strategies have been proposed to accelerate proton transport, for example by introducing vacancies, incorporating catalytic metals or chemically functionalizing the lattice. However, these techniques can compromise other properties, such as ion selectivity or mechanical stability. Here we show that independent control of the electric field, E, at around 1 V nm-1, and charge-carrier density, n, at around 1 x 10^14 cm-2, in double-gated graphene allows the decoupling of proton transport from lattice hydrogenation and can thereby accelerate proton transport such that it approaches the limiting electrolyte current for our devices. Proton transport and hydrogenation can be driven selectively with precision and robustness, enabling proton-based logic and memory graphene devices that have on-off ratios spanning orders of magnitude. Our results show that field effects can accelerate and decouple electrochemical processes in double-gated 2D crystals and demonstrate the possibility of mapping such processes as a function of E and n, which is a new technique for the study of 2D electrode-electrolyte interfaces.

We explore the conformal 5D braneworld, where warping emerges through conformal symmetry breaking. Our scenario seamlessly aligns with conventional brane approaches if conformal symmetry remains unbroken. It is shown that a model with a single conformal breaking parameter effectively localizes gravity on the brane, but it falls short in trapping gauge bosons. However, in scenarios with two parameters, gravity is localized, and the model also achieves the localization of zero modes for both gauge and Dirac fields.

We use the density matrix renormalization group (DMRG) and a hard-core boson map to investigate the quantum phase transitions present in the phase diagram of the frustrated Heisenberg ladder in a magnetic field. The quantum bicritical point is observed at the end of a first-order transition line, which is at the meeting of the two second-order transition lines that bound the fully polarized plateau. The characterization of the bicritical point was made using a hard-core boson mapping of the low-energy excitations from the fully polarized phase and through DMRG by studying the probability density of finding the rung spins in a singlet or a triplet state with zero spin component along the magnetic field. In particular, we give conditions for the exchange couplings for the presence of the first-order transition line and the bicritical point in the phase diagram. Moreover, we unveil the phase-separated states for magnetization values inside the magnetization jump and, in particular, the dependence on the system size of the energy curve as a function of magnetization. Finite-size scaling analysis of the transverse spin correlation functions has been used to estimate the critical points of the Kosterlitz-Thouless transitions from the fractional magnetization plateau $m=1/2$ to the respective gapless Luttinger liquid phases for some sets of parameters., Comment: 14 pages, 14 figures

The interplay between a magnetic field and the Coulomb potential from a charged vacancy on the electron states in graphene is investigated within the tight-binding model. The Coulomb potential removes locally Landau level degeneracy, while the vacancy introduces a satellite level next to the normal Landau level. These satellite levels are found throughout the positive energy region, but in the negative energy region they turn into atomic collapse resonances. Crossings between Landau levels with different angular quantum number $m$ are found. Unlike the point impurity system in which an anticrossing occurs between Landau levels of the same $m$, in this work anticrossing is found between the normal Landau level and the vacancy induced level. The atomic collapse resonance hybridize with the Landau levels. The charge at which the lowest Landau level $m = -1, N = 1$ crosses increases $E = 0$ with enhancing magnetic field. Landau level scaling anomaly occurs when the charge is larger than the critical charge $\beta\approx0.6$ and this critical charge is independent of the magnetic field.

This article gives a necessary first step to understanding the critical set phenomenon for the Korteweg-de Vries (KdV) equation posed on interval $[0,L]$ considering the Neumann boundary conditions with only one control input. We showed that the KdV equation is controllable in the critical case, i.e., when the spatial domain $L$ belongs to the set $\mathcal{R}_c$, where $c\neq-1$ and $$ \mathcal{R}_c:=\left\{\frac{2\pi}{\sqrt{3(c+1)}}\sqrt{m^2+ml+m^2};\ m,l\in \mathbb{N}^*\right\}\cup\left\{\frac{m\pi}{\sqrt{c+1}};\ m\in \mathbb{N}^*\right\}, $$ the KdV equation is exactly controllable in $L^2(0,L)$. The result is achieved using the return method together with a fixed point argument., Comment: 24 pages, 1 figure. Comments are welcome

This article presents some controllability and stabilization results for a system of two coupled linear Schr\"odinger equations in the one-dimensional case where the state components are interacting through the Kirchhoff boundary conditions. Considering the system in a bounded domain, the null boundary controllability result is shown. The result is achieved thanks to a new Carleman estimate, which ensures a boundary observation. Additionally, this boundary observation together with some trace estimates, helps us to use the Gramian approach, with a suitable choice of feedback law, to prove that the system under consideration decays exponentially to zero at least as fast as the function $e^{-2\omega t}$ for some $\omega>0$., Comment: 21 pp - Some new references and minor changes were made. Comments are welcome

This work builds upon the previous article [1] and explores the solution of the charged black string introduced in [2]. The black bounce regularization method, based on the Simpson-Visser solution, is employed by transforming the radial variable using $r\rightarrow \sqrt{r^2+a^2}$. The regular charged black string metric is defined, and the properties of event horizons, surface gravity, and Hawking temperature are investigated. The behavior of curvature quantities, including curvature invariants and tensors, is examined to verify the absence of singularities when $a\neq 0$. The Einstein equation for the energy-momentum tensor is solved, and the null energy condition is analyzed for the obtained solution. The sources of this solution are evaluated, combining a scalar field with nonlinear electrodynamics. However, unlike other works, an electric field is considered instead of a magnetic field. Finally, the study calculates the possibility of stable or unstable circular orbits for massive and massless particles., Comment: 7 pages

In this paper, we study black strings in asymptotic safety gravity (ASG) scenario. The ASG approach is introduced by implementing gravitational and cosmological running coupling constants directly in the black string metric. We calculate the Hawking temperature, entropy, and heat capacity of the improved black string metric in two cases: considering the cosmological constant fixed in some fixed point and the general case where both Newton's constant and cosmological constant are improved. For the identification of the scale moment we used an general inverse law setting $k(r)\sim 1/r^{n}$. We show that improving only the Newton's constant the problem of singularity is solved for the identifications with $n>1$. However, if the cosmological constant is also running the singularity persists in the solution. Also, we show that the ASG effects predicts the presence of a remnant mass in the final evaporation process. Besides that, a logarithmic correction is observed in the entropy. However, a running cosmological constant introduces new correction terms to the entropy beyond that. We show that the improved black string solution remains stable, as in the usual case. Phase transitions are not observed in both cases studied here., Comment: 18 pages, 9 figures

In this paper, we investigate the spinless stationary Schr\"odinger equation for the electron when it is permanently bound to a generalized Ellis-Bronnikov graphene wormhole-like surface. The curvature gives rise to a geometric potential affecting thus the electronic dynamics. The geometry of the wormhole's shape is controlled by the parameter $n$ which assumes even values. We discuss the role played by the parameter $n$ and the orbital angular momentum on bound states and probability density for the electron., Comment: 9 pages, 6 figures, two columns

The density matrix renormalization group and quantum Monte Carlo method are used to describe coupled trimer chains in a magnetic field h. The Hamiltonian contains exchange terms involving the intra-trimer coupling J1 (taken as the unit of energy) and the inter-trimer coupling J2, plus the Zeeman interaction for a magnetic field h along the z direction. Results for the magnetization per trimer m are calculated in regimes of positive and negative values of the ratio J = J2 / J1, from which the rich field-induced ground state phase diagram h vs. J is derived, with the presence of Luttinger liquid, the 1/3-plateau (m = 1/2), and the one of fully polarized magnetization (m = 3/2). Also, the zero-field Lanczos calculation of spin-wave dispersion from the 1/3-plateau for $S^z = 1$ is shown at the previous regimes of J values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0

In this paper we find an universal mass scale for all $p-$forms in multi-brane worlds model. It is a known fact the this model provides an ultralight mode for the fields. However, to get this, the Lagrangians considered in the literature are not covariant. In order to solve this, we propose a covariant version to multi-localize $q-$form fields. As a consequence of the covariance, we show that all the $q$-form fields have an ultralight mode with the same mass that the gravitational one. That way we show that there is an universal mass scale for the ultralight modes of the bosonic fields. This suggests that a new physics must emerge, for all theses fields, at the same scale. After that, we revisit the results that consider a crystal manyfold background in the Randall-Sundrum scenary (RS), and add the discussion related to geometrical couplings in such a configuration. The wave functions of fields trapped in the crystal are Bloch-like waves, and their behavior is very similar to electrons inside a lattice, just like in the Kronig-Penney model (KP). We compute the mass dispersion relations for those fields with and without a dilaton coupling. It leads to new results for the band gap structure of these fields. In the case of the Kalb-Ramond field, and with the correct dispersion relation, there is no gap between the mass bands. Also, always that the field is coupled with the dilaton, its first mass mode decreases. When the generalization to the $q-$form is done, we show that it is not possible to suppress or generate mass for the fields by controlling the dilaton coupling, differently of what was argued previously., Comment: It should be a replacement of arXiv:2009.07197

We compare the ground-state features of alternating ferrimagnetic chains $(1/2, S)$ with $S=1,3/2,2,5/2$ in a magnetic field and the corresponding Holstein-Primakoff bosonic models up to order $\sqrt{s/S}$, with $s=1/2$, considering the fully polarized magnetization as the boson vacuum. {The single-particle Hamiltonian is a Rice-Mele model with uniform hopping and modified boundaries, while the interactions have a correlated (density-dependent) hopping term and magnon-magnon repulsion.} The magnon-magnon repulsion increases the many-magnon energy and the density-dependent hopping decreases the kinetic energy. We use density matrix renormalization group calculations to investigate the effects of these two interaction terms in the bosonic model{, and display the quantitative agreement between the results from the spin model and the full bosonic approximation. In particular, we verify the good accordance in the behavior of the edge states, associated with the ferrimagnetic plateau, from the spin and from the bosonic models. Furthermore, we show that the boundary magnon density strongly depends on the interactions and particle statistics., Comment: 13 pages, 6 figures

This paper presents the effects of Lorentz violation in superconductivity. Constructing a Lorentz-Violating Ginzburg-Landau theory of superconductivity we discuss the influence of the Lorentz-Violating tensors $\hat{k}_{c}^{ij}$ and $\hat{k}_a^i$ in the London's depth penetration, in the coherence length and critical magnetic field., Comment: 5 pages, 1 figure, two columns. Matches version to be published at EPL

Quantum many-body edge and extended magnon excitations from the 1/3 -- plateau of the anisotropic Heisenberg model on an open AB$_2$ chain in a magnetic field $h$ are unveiled using the density matrix renormalization group and exact diagonalization. By tuning both the anisotropy and $h$ in the rich phase diagram, the edge states penetrate in the bulk, whose gap closes in a symmetry-protected topological Kosterlitz-Thouless transition. Also, we witness the squeezed chain effect, the breaking of the edge states degeneracy, and a topological change of the excitations from gapped magnons with quadratic long-wavelength dispersion to a linear spinon dispersion in the Luttinger liquid gapless phase as the anisotropy $\lambda$ approaches the critical point from the $\lambda>0$ side of the phase diagram., Comment: 10 pages, 10 figures

A charged particle in the presence of a magnetic field is studied in the position dependent operator formalism. Instead of a quantum harmonic oscillator, the solution of the resulting Schr\"odinger-like equation is the one for the Morse oscillator. The anharmonicity that shows up naturally from the theory is analogous to the corrections introduced by relativistic ones.The degeneracy of the spin up and down levels is lifted due to the non-Euclidean space. It is shown that the Fermi energy and the total ground state energy of the 2DEG is also modified., Comment: 4 pages, 4 figures

Precise measurement of the angular deviation of an object is a common task in science and technology. Many methods use light for this purpose. Some of these exploit interference effects to achieve technological advantages, such as amplification effects, or simplified measurement devices. However, all of these schemes require phase stability to be useful. Here we show theoretically and experimentally that this drawback can be lifted by utilizing two-photon interference, which is known to be less sensitive to phase fluctuations. Our results show that non-classical interference can provide a path towards robust interferometric sensing, allowing for increased metrological precision in the presence of phase noise., Comment: Accepted at Physical Review Applied

We investigate interferometric techniques to estimate the deflection angle of an optical beam and compare them to the direct detection of the beam deflection. We show that quantum metrology methods lead to a unifying treatment for both single photons and classical fields. Using the Fisher information to assess the precision limits of the interferometric schemes, we show that the precision can be increased by exploiting the initial transverse displacement of the beam. This gain, which is present for both Sagnac and Mach-Zehnder-like configurations, can be considerable when compared to non-interferometric methods. In addition to the fundamental increase in precision, the interferometric schemes have the technical advantage that (i) the precision limits can be saturated by a sole polarization measurement on the field, and that (ii) the detection system can be placed at any longitudinal position along the beam. We also consider position-dependent polarization measurements, and show that in this case the precision increases with the propagation distance, as well as the initial transverse displacement., Comment: Comments are welcome

This paper presents divergent contributions of the radiative corrections for a Lorentz-violating extension of the scalar electrodynamics. We initially discuss some features of the model and extract the Feynman rules. Then we compute the one-loop radiative corrections using Feynman parametrization and dimensional regularization in order to evaluate the integrals. We also discuss Furry's theorem validity and renormalization in the present context.

The use of the adiabatic approximation in practical applications, as in adiabatic quantum computation, demands an assessment of the errors made in finite-time evolutions. Aiming at such scenarios, we derive bounds relating error and evolution time in the adiabatic approximation that go beyond typical scaling relations. Using the Adiabatic Perturbation Theory, we obtain leading-order expressions valid for long evolution time $T$, while explicitly determining the shortest time $T$ and the largest error $\varepsilon$ for which they are valid. In this validity regime, we can make clear and precise statements about the evolution time needed to reach a given error and vice-versa. As an example of practical importance, we apply these results to the adiabatic search, and obtain for the first time an error-run-time trade-off relation that fully reproduces the discrete-Grover-search scaling. We also pioneer the obtention of tight numerical values for $\varepsilon$ and $T$ under the error-reducing strategy ``boundary cancelation''., Comment: Main text 16 pages, 26 pages total (with appendix), 3 figures

We use density matrix renormalization group to study the first-order quantum phase transition induced by a magnetic field $h$ in a frustrated ferrimagnetic chain. The magnetization ($m$) curve as a function of $h$ presents a macroscopic jump and the energy curve as a function of $m$ has two global minima. We characterize the two competing phases and study the phase-separated states in the coexistence region. Also, we observe that the transition is accompanied by an increase in the number of itinerant singlet pairs between sites in the unit cells of the chain. Finally, we identify the critical point at the end of the first-order transition line and a crossover line., Comment: 7 pages, 5 figures

Quantum critical (QC) phenomena can be accessed by studying quantum magnets under an applied magnetic field ($B$). The QC points are located at the endpoints of magnetization plateaus and separate gapped and gapless phases. In one dimension, the low-energy excitations of the gapless phase form a Luttinger liquid (LL), and crossover lines bound insulating (plateau) and LL regimes, as well as the QC regime. Alternating ferrimagnetic chains have a spontaneous magnetization at $T=0$ and gapped excitations at zero field. Besides the plateau at the fully polarized (FP) magnetization; due to the gap, there is another magnetization plateau at the ferrimagnetic (FRI) magnetization. We develop spin-wave theories to study the thermal properties of these chains under an applied magnetic field: one from the FRI classical state, and other from the FP state, comparing their results with quantum Monte Carlo data. We deepen the theory from the FP state, obtaining the crossover lines in the $T$ vs. $B$ low-$T$ phase diagram. In particular, from local extreme points in the susceptibility and magnetization curves, we identify the crossover between an LL regime formed by excitations from the FRI state to another built from excitations of the FP state. These two LL regimes are bounded by an asymmetric dome-like crossover line, as observed in the phase diagram of other quantum magnets under an applied magnetic field., Comment: 10 pages, 8 figures

Bethe ansatz and bosonization procedures are used to describe the thermodynamics of the strong-coupled Hubbard chain in the \textit{spin-incoherent} Luttinger liquid (LL) regime: $J(\equiv 4t^2/U)\ll k_B T\ll E_F$, where $t$ is the hopping amplitude, $U(\gg t)$ is the repulsive on-site Coulomb interaction, and $k_B T (E_F\sim t)$ is the thermal (Fermi) energy. We introduce a fractional Landau LL approach, whose $U=\infty$ fixed point is exactly mapped onto an ideal gas with two species obeying the Haldane-Wu \textit{exclusion} fractional statistics. This phenomenological approach sheds light on the behavior of several thermodynamic properties in the spin-incoherent LL regime: specific heat, charge compressibility, magnetic susceptibility, and Drude weight. In fact, besides the hopping (mass) renormalization, the fractional Landau LL parameters, due to quasiparticle interaction, are determined and relationships with velocities of holons and spinons are unveiled. The specific heat thus obtained is in very good agreement with previous density matrix renormalization group (DMRG) simulations of the $t$-$J$ model in the spin-incoherent regime. A phase diagram is provided and two thermodynamic paths to access this regime clarifies both the numerical and analytical procedures. Further, we show that the high-$T$ limit of the fractional Landau LL entropy and chemical potential exhibit the expected results of the $t$-$J$ model, under the condition $U\gg k_B T$. Lastly, finite-temperature Lanczos simulations of the single-particle distribution function confirm the characteristics of the spin-incoherent regime and the high-$T$ limit observed in previous DMRG studies., Comment: 16 pages, 6 figures

In this manuscript we compute corrections to the global Casimir effect at zero and finite temperature due to Rainbow's Gravity (parametrized by $\xi$). For this we use the solutions for the scalar field with mass $m$ in the deformed Schwarzschild background and the corresponding quantized energies of the system, which represent the stationary states of the field and yield the stable part of the quantum vacuum energy. The analysis is made here by considering the limit for which the source mass, $M$, approaches zero, in order to verify the effects on the global Casimir effect in mini black holes near to the Planck scale, $\omega_P$. We find a singular behavior for the regularized vacuum energy at zero temperature and for all the corresponding thermodynamic quantities when $m^2=\omega^2_P/\xi$, what can be seen as the limit of validity of the model. Furthermore, we show that the remnant Casimir tension over the event horizon in the limit $M\to 0$ is finite for any temperature and all the space of parameters. In fact we show that the remnant tension receives no corrections from Rainbow's Gravity. This points to the fact that such a behavior may be an universal property of this kind of system., Comment: Version accepted for publication in EPJP

Cross sections for elastic and inelastic scattering of the weakly-bound $^9$Be nucleus on a $^{120}$Sn target have been measured at seven bombarding energies around and above the Coulomb barrier. The elastic angular distributions are analyzed with a four-body continuum-discretized coupled-channels (CDCC) calculation, which considers $^9$Be as a three-body projectile ($\alpha$ + $\alpha$ + n). An optical model analysis using the S\~ao Paulo potential is also shown for comparison. The CDCC analysis shows that the coupling to the continuum part of the spectrum is important for the agreement with experimental data even at energies around the Coulomb barrier, suggesting that breakup is an important process at low energies. At the highest incident energies, two inelastic peaks are observed at 1.19(5) and 2.41(5) MeV. Coupled-channels (CC) calculations using a rotational model confirm that the first inelastic peak corresponds to the excitation of the 2$_1^+$ state in $^{120}$Sn, while the second one likely corresponds to the excitation of the 3$_1^-$ state., Comment: 11 pages, 9 figures. Accepted as PRC

Trying to quantize the string in a de Sitter spacetime, Miao Li, Wei Song and Yushu Song presents a solution for the string equation of motion (JHEP04(2007)042) that is not correct. This reopens the problem by them addressed., Comment: 4 pages

A family of Boussinesq systems has been proposed to describe the bi-directional propagation of small amplitude long waves on the surface of shallow water. In this paper, we investigate the well-posedness and boundary stabilization of the generalized higher order Boussinesq systems of Korteweg-de Vries--type posed on a interval. We design a two-parameter family of feedback laws for which the system is locally well-posed and the solutions of the linearized system are exponentially decreasing in time., Comment: 26 pg

Hyperentanglement --- simultaneous entanglement between multiple degrees of freedom of two or more systems --- has been used to enhance quantum information tasks such as quantum communication and photonic quantum computing. Here we show that hyperentanglement can lead to increased quantum advantage in metrology, with contributions from the entanglement in each degree of freedom, allowing for Heisenberg scaling in the precision of parameter estimation. Our experiment employs photon pairs entangled in polarization and spatial degrees of freedom to estimate a small tilt angle of a mirror. Precision limits beyond shot noise are saturated through a simple binary measurement of the polarization state. The broad validity of the dynamics considered here implies that similar strategies based on hyperentanglement can offer improvement in a wide variety of metrological tasks., Comment: 6 pages, 4 figures

In this paper we consider the initial boundary value problem of the Korteweg-de Vries equation posed on a finite interval \begin{equation} u_t+u_x+u_{xxx}+uu_x=0,\qquad u(x,0)=\phi(x), \qquad 00 \qquad (1) \end{equation} subject to the nonhomogeneous boundary conditions, \begin{equation} B_1u=h_1(t), \qquad B_2 u= h_2 (t), \qquad B_3 u= h_3 (t) \qquad t>0 \qquad (2) \end{equation} where \[ B_i u =\sum _{j=0}^2 \left(a_{ij} \partial ^j_x u(0,t) + b_{ij} \partial ^j_x u(L,t)\right), \qquad i=1,2,3,\] and $a_{ij}, \ b_{ij}$ $ (j,i=0, 1,2,3)$ are real constants. Under some general assumptions imposed on the coefficients $a_{ij}, \ b_{ij}$, $ j,i=0, 1,2,3$, the IBVPs (1)-(2) is shown to be locally well-posed in the space $H^s (0,L)$ for any $s\geq 0$ with $\phi \in H^s (0,L)$ and boundary values $h_j, j=1,2,3$ belonging to some appropriate spaces with optimal regularity., Comment: 28 pages