Semiclassical Regime Research Articles

Semiclassical quantization of the superstring and Hagedorn temperature

In a recent paper [1], the semiclassical quantization of a string, winding once around the compact Euclidean time circle, on a supergravity background dual to the deep infrared regime of a confining finite temperature gauge theory, was carried out. The string mass-shell condition and, by extrapolation, the Hagedorn temperature to leading order in the holographic limit was deduced. In this work, we improve on those results in three ways. First, we fix some missing details of the related light-cone quantization analysis. Second, we reconsider the problem under the lens of a background-covariant geometrical formalism. This allows us to put the semiclassical mass-shell condition on more solid grounds. Finally, going beyond the semiclassical regime, we compute the Hagedorn temperature at next-to-leading order in the holographic limit. The sub-leading correction turns out to arise entirely from the contribution of the zero modes of the massive worldsheet scalar fields. Our result matches that of a recent analysis in the literature based on the Horowitz-Polchinski stringy star effective model.

On a neural network approach for solving potential control problem of the semiclassical Schrödinger equation

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schrödinger equation, where the control variable is the potential given by an external field that may contain uncertainties. Inspired by a relevant work Li et al., 2021 [1], we incorporate the sampling-based learning process into the training of networks, while combining with the fast time-splitting spectral method for the Schrödinger equation in the semi-classical regime. The numerical results have shown the efficiency and accuracy of our proposed deep learning approach.

Rogue wave formation scenarios for the focusing nonlinear Schrödinger equation with parabolic-profile initial data on a compact support.

We study the (1+1) focusing nonlinear Schrödinger equation for an initial condition with compactly supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blowup in finite time, generalizing a result by Talanov etal. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semiclassical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time. The sign of the chirp appears to determine the prevailing scenario among two competing mechanisms for rogue wave formation. For negative values, the numerical simulations are suggestive of the dispersive regularization of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seems to result from the interaction of counterpropagating dispersive dam break flows, as in the box problem recently studied by El, Khamis, and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics.

Enhancing quantum synchronization through homodyne measurement, noise, and squeezing.

Quantum synchronization has been a central topic in quantum nonlinear dynamics. Despite the rapid development in this field, very few have studied how to efficiently boost synchronization. Homodyne measurement emerges as one of the successful candidates for this task but preferably in the semiclassical regime. In our work, we focus on the phase synchronization of a harmonic-driven quantum Stuart-Landau oscillator and show that the enhancement induced by homodyne measurement persists into the quantum regime. Interestingly, optimal two-photon damping rates exist when the oscillator and driving are at resonance and with a small single-photon damping rate. We also report noise-induced enhancement in quantum synchronization when the single-photon damping rate is sufficiently large. Apart from these results, we discover that adding a squeezing Hamiltonian can further boost synchronization, especially in the semiclassical regime. Furthermore, the addition of squeezing causes the optimal two-photon pumping rates to shift and converge.

Evolution of the wave function's shape in a time-dependent harmonic potential

Abstract An effective operational approach to quantum mechanics is to focus on the evolution of wave packets, for which the wave function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of freedom describing the shape of the wave packet and its fluctuations. These quantum dressing are independent degrees of freedom, mathematically encoded in the higher moments of the wave function. We review how to extract the effective dynamics for Gaussian wave packets evolving according to the Schrödinger equation with time-dependent potential in a 1 + 1-dimensional spacetime, and derive the equations of motion for the quadratic uncertainty. We then show how to integrate the evolution of all the higher moments for a general wave function in a time-dependent harmonic potential.

Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential

Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only |cdot | hat{V} in ell ^1 (mathbb {Z}^3). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy.

Spectral Analysis of Discrete Metastable Diffusions

We consider a discrete Schrödinger operator H_varepsilon = -varepsilon ^2Delta _varepsilon + V_varepsilon on ell ^2(varepsilon mathbb {Z}^d), where varepsilon >0 is a small parameter and the potential V_varepsilon is defined in terms of a multiwell energy landscape f on mathbb {R}^d. This operator can be seen as a discrete analog of the semiclassical Witten Laplacian of mathbb {R}^d. It is unitarily equivalent to the generator of a diffusion on varepsilon mathbb {Z}^d, satisfying the detailed balance condition with respect to the Boltzmann weight exp {(-f/varepsilon )}. These type of diffusions exhibit metastable behavior and arise in the context of disordered mean field models in Statistical Mechanics. We analyze the bottom of the spectrum of H_varepsilon in the semiclassical regime varepsilon ll 1 and show that there is a one-to-one correspondence between exponentially small eigenvalues and local minima of f. Then we analyze in more detail the bistable case and compute the precise asymptotic splitting between the two exponentially small eigenvalues. Through this purely spectral-theoretical analysis of the discrete Witten Laplacian we recover in a self-contained way the Eyring–Kramers formula for the metastable tunneling time of the underlying stochastic process.

Thermodynamic uncertainty relations in mesoscopic devices.

We investigate the thermodynamic uncertainty relations (TURs) in mesoscopic devices for all universal symmetry classes of Wigner-Dyson and Dirac (chiral). The observables of interest include the TUR (MS), which is defined in terms of the ratio between the mean noise and mean conductance, as well as a new TUR (R) proposed in this article, which is based on the ensemble mean of the noise-to-conductance ratio. A detailed study is made on the quantum interference corrections associated with the TURs. We also analyze the influence of orbital and sublattice/chiral degrees of freedom for the validity of the observables in these chaotic mesoscopic billiards. Our investigation is based on the concatenation between the Landauer-Büttiker theory, the Mahaux-Wendeinmüller theory, and the TURs. We simulate the universal mesoscopic chaotic quantum dots using the random-matrix theory and compare our numerical results with the pertinent experimental data. The results were obtained for a different number of channels and tunneling rates that vary from the opaque to the ideal regime and, in all cases, demonstrate a clear phenomenological distinction between the TURs. In particular, the opaque regime engenders remarkable differences between the observables, even in the semiclassical regime, which characterizes a clear violation of the central limit theorem. Furthermore, we show that the phenomenology of the quantum interference corrections is strikingly robust, surprisingly exhibiting an order of magnitude greater than the supposedly leading semiclassical term for the TUR (R).

Semiclassical analysis of quantum asymptotic fields in the Yukawa theory

In this article, we study the asymptotic fields of the Yukawa particle-field model of quantum physics, in the semiclassical regime $\hslash\to 0$, with an interaction subject to an ultraviolet cutoff. We show that the transition amplitudes between final (respectively initial) states converge towards explicit quantities involving the outgoing (respectively incoming) wave operators of the nonlinear Schr\odinger-Klein-Gordon (S-KG) equation. Thus, we rigorously link the scattering theory of the Yukawa model to that of the Schr\odinger-Klein-Gordon equation. Moreover, we prove that the asymptotic vacuum states of the Yukawa model have a phase space concentration property around classical radiationless solutions. Under further assumptions, we show that the S-KG energy admits a unique minimizer modulo symmetries and identify exactly the semiclassical measure of Yukawa ground states. Some additional consequences of asymptotic completeness are also discussed, and some further open questions are raised.

Stochastic theory of charge dynamics and recombination in defect clusters in bulk silicon

Various types of defect clusters are generated in bulk Si-based high-energy particle detectors. They become either recombination centres or charge trapping centres. Populated trapping centres create internal fields which may affect the dynamics and recombination of remaining free charges. In the semiclassical regime, the charge dynamics can be described by the Boltzmann equation. In this paper, the stochastic description is presented as an alternative to a direct solution of the Boltzmann equation approach. It is demonstrated that the hole dynamics can be described in the overdamped regime in both light-hole and heavy-hole cases. Electrons have to be described by including ballistic components. The theory allows an efficient simulation of the electron and hole dynamics in the vicinity of a defect cluster and demonstrates that local trapping centres are the major components enabling fast charge recombinations. The dipolar type internal fields of permanently trapped charges only weakly influence the charge recombination kinetics.

Systematic study of tunable laser cooling for trapped-ion experiments

We report on a comparative analysis of quenched sideband cooling in trapped ions. We introduce a theoretical approach for time-efficient simulation of the temporal cooling characteristics and derive the optimal conditions providing fast laser cooling into the ion’s motional ground state. The simulations were experimentally benchmarked with a single 172Yb+ ion confined in a linear Paul trap. Sideband cooling was carried out on a narrow quadrupole transition, enhanced with an additional clear-out laser for controlling the effective linewidth of the cooling transition. Quench cooling was thus for the first time studied in the resolved sideband, intermediate and semi-classical regime. We discuss the non-thermal distribution of Fock states during laser cooling and reveal its impact on time dilation shifts in optical atomic clocks.

Lévy flight for electrons in graphene: Superdiffusive-to-diffusive transport transition

In this work we propose an electronic L\'evy flight device, analogous to a recent optical realization. To that end, we investigate the transmission of electrons in graphene nanoribbons in the presence of circular electrostatic clusters, whose diameter follow a power-law distribution. We analyze the effect of the electrostatic clusters on the electronic transport regime of the nanoribbons, in terms of its diffusion behavior. Our numerical calculations show that the presence of circular electrostatic clusters induces a transition from L\'evy (superdiffusive) to diffusive transport as the energy increases. Furthermore, we argue that in our electronic L\'evy flight device, superdiffusive transport is an exclusive feature of the low-energy quantum regime, while diffusive transport is a feature of the semiclassical regime. Therefore, we attribute the observed transition to the chiral symmetry breaking, once the energy moves away from the Dirac point of graphene.

Meson content of entanglement spectra after integrable and nonintegrable quantum quenches

We use tensor network simulations to calculate the time evolution of the lower part of the entanglement spectrum and return rate functions after global quantum quenches in the Ising model. We consider ground state quenches towards mesonic parameter ranges with confined fermion pairs as nonperturbative bound states in a semiclassical regime and the relativistic E$_8$ theory. We find that in both cases only the dominant eigenvalue of the modular Hamiltonian fully encodes the meson content of the quantum many-body system or quantum field theory, giving rise to nearly identical entanglement oscillations in the entanglement entropy. When the initial state is prepared in the paramagnetic phase, the return rate density exhibits regular cusps at unequally spaced positions, signaling the appearance of dynamical quantum phase transitions, at which the entanglement spectrum remains gapped. Our analyses provide a deeper understanding on the role of quantum information quantities for the dynamics of emergent phenomena reminiscent of systems in high-energy physics.

Quantum singularities

Two spatial regions $B$ and $R$ are hyperentangled if the generalized entropy satisfies $S_{\text{gen}}^{B\cup R}<S_{\text{gen}}^R$. If in addition all future (or all past) directed inward null shape deformations of $B$ decrease $S_{\text{gen}}^{B\cup R}$, then we show that the causal development of $B$, with $R$ held fixed, must be incomplete. This result eliminates the Null Energy Condition from the assumptions of a recently proven singularity theorem. Instead, we assume a quantum version of the Bousso bound. Taking $R$ to contain the Hawking radiation after the Page time, our theorem predicts a singularity in the past causal development of the black hole interior. This is surprising because the classical spacetime is nonsingular in the past. However, one finds that Cauchy slices that are required to contain $R$ do not remain in the semiclassical regime. The quantum singularities predicted by our theorem are an obstruction to further semiclassical evolution, generalizing the singularities of classical general relativity.

Cauchy slice holography: a new AdS/CFT dictionary

We investigate a new approach to holography in asymptotically AdS spacetimes, in which time rather than space is the emergent dimension. By making a sufficiently large T2-deformation of a Euclidean CFT, we define a holographic theory that lives on Cauchy slices of the Lorentzian bulk. (More generally, for an arbitrary Hamiltonian constraint equation that closes, we show how to obtain it by an irrelevant deformation from a CFT with suitable anomalies.) The partition function of this theory defines a natural map between the bulk canonical quantum gravity theory Hilbert space, and the Hilbert space of the usual (undeformed) boundary CFT. We argue for the equivalence of the ADM and CFT Hamiltonians. We also explain how bulk unitarity emerges naturally, even though the boundary theory is not reflection-positive. This allows us to reformulate the holographic principle in the language of Wheeler-DeWitt canonical quantum gravity.Along the way, we outline a procedure for obtaining a bulk Hilbert space from the gravitational path integral with Dirichlet boundary conditions. Following previous conjectures, we postulate that this finite-cutoff gravitational path integral agrees with the T2-deformed theory living on an arbitrary boundary manifold — at least near the semiclassical regime. However, the T2-deformed theory may be easier to UV complete, in which case it would be natural to take it as the definition of nonperturbative quantum gravity.

Quantum oscillations as a robust fingerprint of chiral anomaly in nonlinear response in Weyl semimetals

In view of searching the signature of the celebrated chiral anomaly (CA) in Weyl semimetals (WSMs) in ongoing experiments, quantum oscillation in linear response regime has been considered as an important signature in the magneto transports in WSMs, due to its unique relation to CA. Investigating the nonlinear planar effects (NPEs) starting from the semiclassical regime to the ultra-quantum limit within the framework of Boltzmann transport theory incorporating Landau quantization, we here propose the quantum oscillations in NPEs can serve as a robust signature of CA in WSMs. By obtaining analytical expressions, we show that the quantum oscillations of the nonlinear effects exhibit two different period scales in 1/B (B is the magnetic field) compared to the linear responses where only one period scale exists. We find that these quantum oscillations in NPEs are attributed to the deviation of chiral chemical potential (CCP), which is proportional to the finite band tilt as well as transverse electric field and therefore, directly linked to CA in WSMs. In addition, we also show that the CA-induced nonlinear magneto conductivity is linear and independent in the magnetic field in the semiclassical and ultraquantum regimes, respectively. We conclude that the proposed behaviors of NPEs in different regimes uniquely signify the existence of CA and therefore, can serve as a probe of identifying CA in WSMs in experiments.

The gaugino condensate from asymmetric four-torus with twists

We calculate the gaugino condensate in SU(2) super Yang-Mills theory on an asymmetric four-torus \U0001d54b4 with ’t Hooft’s twisted boundary conditions. The \U0001d54b4 asymmetry is controlled by a dimensionless detuning parameter ∆, proportional to L3L4 − L1L2, with Li denoting the \U0001d54b4 periods. We perform our calculations via a path integral on a \U0001d54b4. Its size is taken much smaller than the inverse strong scale Λ and the theory is well inside the semi-classical weak-coupling regime. The instanton background, constructed for ∆ ≪ 1 in [1], has fractional topological charge Q=frac{1}{2} and supports two gaugino zero modes, yielding a non-vanishing bilinear condensate, which we find to be ∆-independent. Further, the theory has a mixed discrete chiral/1-form center anomaly leading to double degeneracy of the energy eigenstates on any size torus with ’t Hooft twists. In particular, there are two vacua, ∣0〉 and ∣1〉, that are exchanged under chiral transformation. Using this information, the ∆-independence of the condensate, and assuming further that the semi-classical theory is continuously connected to the strongly-coupled large-\U0001d54b4 regime, we determine the numerical coefficient of the gaugino condensate: 〈0|trλλ|0〉 = ∣〈1|trλλ|1〉∣ = 32π2Λ3, a result equal to twice the known ℝ4 value. We discuss possible loopholes in the continuity approach that may lead to this discrepancy.

Controlling Quantum Chaos: Optimal Coherent Targeting.

One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime, but requires tailored perturbations whose effects must undo the dynamical spreading of the evolving quantum state. The procedure described here is applied to initially minimum uncertainty wave packets in the quantum kicked rotor, a preeminent quantum chaotic paradigm, to illustrate the method, and investigate its accuracy. The method's error can be made to vanish as ℏ→0.

The paradigm of quantum cosmology through Dunkl fractional Laplacian operators and fractal dimensions

The semi-classical regime of fractional quantum cosmology has been discussed based on the Wheeler-DeWitt equation and ADM-Hamiltonian formalism. Fractionality has been introduced through two different approaches: the first one is based on fractional Dunkl Laplacian operator and the second one based on fractal calculus. Our models generalize the recent approaches of fractional quantum cosmology introduced in literature. In the first approach, it was revealed that power-law inflation and large number of e-folds may be obtained for various values of the fractional parameter. However, the second approach is plausible only if the cosmological constant decays with the scale factor of the universe. We have confronted our model with observations based on the Bayesian hierarchical model that describes the full distance ladder from nearby geometric anchors through Cepheids to Hubble-Flow SNe we have estimated the numerical values of the fractional order parameter. In both scenarios, the number of e-folds is too large.Pacs numbers: 05.45.Df, 45.10.Hj, 98.80.-k

Spin parity effects in a monoaxial chiral ferromagnetic chain

While spin parity effects, physics crucially depending on whether the spin quantum number $S$ is half-odd integral or integral, have for decades been a source of new developments for the quantum physics of antiferromagnetic spin chains, the investigation into their possible ferromagnetic counterparts has remained largely unchartered, especially in the fully quantum (as opposed to the semiclassical) regime. Here we present such studies for monoaxial chiral ferromagnetic spin chains. We start by examining magnetization curves for finite-sized systems, where a magnetic field is applied perpendicular to the helical axis. For half-odd integer $S$, the curves feature discontinuous jumps identified as a series of level crossings, each accompanied by a shift of the crystal momentum $k$ by an amount of $\ensuremath{\pi}$. The corresponding curves for integer valued $S$ are continuous and exhibit crossover processes. For the latter case, $k=0$ throughout. These characteristics are observed numerically when the strength of the Dzyaloshinskii-Moriya interaction (DMI) $D$ is comparable to or larger than that of the ferromagnetic exchange interaction $J$. Solitons are known to be responsible for stepwise changes seen in magnetization curves in the classical limit. These findings therefore prompt us to revise the notion of a soliton, for arbitrary $S$, into a quantum mechanical entity. To unravel this phenomenon at the fully quantum level as is appropriate to spin chains with small $S$, we examine in detail special limiting Hamiltonians amenable to rigorous analysis, consisting of only the DMI and the Zeeman energy. Dubbed the $DH$ model (for $S=\frac{1}{2}$) and the projected $DH$ ($\mathrm{p}DH$) model (for general $S$), they have a set of $2S$ conserved quantities, each of which is the number of solitons of a specific integer-valued height (as measured in the ${S}_{z}$ basis), which ranges from 1 to $2S$. We discuss how to determine the exact crystal momentum of the lowest-energy state belonging to a sector with a given set of the $2S$ soliton numbers. Combined with energetic considerations, this information enables us to reproduce the spin parity effect in the magnetization curves. Finally, we show that the ground states of the special models have substantial numerical overlap with those for generic systems with a finite exchange interaction, suggesting the same physics to be valid there as well.