Imaginary Potential Research Articles

The imaginary potential and entropic force of heavy quarkonia in strongly coupled {mathcal {N}}=4 supersymmetric Yang\u2013Mills plasma on the Coulomb branch

There are two important different mechanisms, the imaginary potential and entropic force, to investigate the dissociation of heavy quarkonia. In this paper, we calculate these two quantities for static and moving quarkonia in the rotating black 3-brane Type IIB supergravity solution dual to {mathcal {N}}=4 super Yang–Mills theory on the Coulomb branch (cSYM) at strong coupling. At Tne 0 , there are two black hole branches: the large and small black hole branches. We investigate the effects of rotating parameter and rapidity for the static and moving quakonium at the large and small black hole branches. We find both mechanisms have the same results. In the large black hole branch: as T/Lambda and beta increase the thermal width decreases and so the suppression becomes stronger. In the small black hole branch: increasing T/Lambda leads to increasing the thermal width and the quarkonium dissociates harder but beta has an opposite effect.

Classical model for survival resonances close to the Talbot time

We present a classical approximation for the peaks of survival resonances occurring when diffracting matter waves from absorption potentials. Generally, our simplified model describes the absorption-diffraction process around the Talbot time very well. Classical treatments of this process are presently lacking. For purely imaginary potentials, the classical model duplicates quantum-mechanical calculations. The classical model allows for simple evolution of phase-space probability densities, which in the limit of the effective Planck constant going to zero allows for a compact analytical expression of the survival probability as a function of remaining parameters. Our work extends the range of processes that can be described through classical analogs.

Topological properties of the one-dimensional <inline-formula><tex-math id="M2">\begin{document}${\cal {PT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M2.png"/></alternatives></inline-formula>-symmetric non-Hermitian spin-orbit-coupled Su-Schrieffer-Heeger model

The topological property and the energy property of one-dimensional non-Hermitian spin-orbit-coupled Su-Schrieffer-Heeger (SSH) model are investigated theoretically, by introducing spin-dependent imaginary potentials with gain and loss effects. It is found that the imaginary potential leads the imaginary energy spectra to appera in the topologically nontrivial region of this system, and the <inline-formula><tex-math id="M5">\begin{document}${\cal {PT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M5.png"/></alternatives></inline-formula> phase transition to happen in the topologically trivial region. In addition, the imaginary potential energy and spin-orbit coupling work together to make the topological phase transition occur in the topologically trivial region, and the topological non-trivial region becomes wider. The energy spectrum results show that the imaginary potential energy and the spin-orbit coupling can obviously control the zero-energy states of the system, which mainly lies in the presence of four zero-energy states with four different localities and numbers. This shows the special adjustment effect of imaginary potential energy and spin-orbit coupling on the energy band structure of the system. It is believed that these results are helpful in understanding the topological phase transition behavior of <inline-formula><tex-math id="M6">\begin{document}${\cal {PT}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M6.png"/></alternatives></inline-formula>-symmetric non-Hermitian system.

Overview of recent lattice QCD results: phase diagram, fluctuations and strangeness

In recent years there has been much progress on the investigation of the QCD phase diagram with lattice QCD. This work will focus on the developments in the last few years with physical parameters and low chemical potential which are obtained by extrapolations from zero or imaginary chemical potential.

Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition

Ample numerical evidence from lattice calculations shows a strong connection between the confining properties of gauge theories at finite temperature and the localisation properties of the low-lying Dirac eigenmodes. In this contribution we discuss recent progress on this topic, focussing on results for QCD at imaginary chemical potential μI/T = π at temperatures above the Roberge-Weiss transition temperature. These confirm the general picture of low modes turning from delocalised to localised at the deconfinement transition, in a previously unexplored setup with a genuine, physical transition in the presence of dynamical fermions. This further supports the use of Dirac eigenmodes as a tool to investigate the mechanisms behind confinement and the deconfinement transition.

«Eyes burn words, words burn eyelids» (Imaginary potential of somatisms in the poetic picture of the world of Mykola Vinhranovskyi)

The article clarifies the peculiarities of the use of somatic units belonging to the general language dictionary; their imaginative potential is revealed in Mykola VinHranovskyi's poetic picture of the world. A wide range of figurative use of somatic lexemes is noted, the semantic specificity of their functioning is substantiated – due to the combination with ethnically marked words-images dream, hope, song, beauty, love, etc.; the introduction of original, unusually modeled tropeic, emotional and evaluative structures. Processes of image formation based on associative convergences of direct and figurative meanings of somatisms, external and internal portraiture of the lyrical "I", actualization of ethnic ideas about female beauty, beauty through the prism of the author's poetic language thinking and aestheticization of semantic plans of somatic lexical units are traced. The range of the figurative potential of somatisms in M. Vinhranovskyi's poetic picture of the world is extremely wide – from lexical-semantic to tropeic and ethnolinguistic paradigms. The key semantic vectors of its objectification are a combination of somatisms with ethnically marked words-images dream, hope, song, beauty, love, etc. The imagery of somatisms is revealed in the composition of originally modeled tropeic, emotive-evaluative, associatively expressed linguistic structures and through the prism of individual authorial aestheticization of the semantic plans of somatic lexical units. The frequency of the use of somatisms enables the characterization of figurative structures centered on "somatism" through chronological-worldview and ethnolinguistic, culturally oriented author's intentions, their objectification and influence on the general expressive plan of the entire expression. The full realization of the imaginative potential of somatisms is provided by contexts in which complex models combining several somatisms are represented. Such figurative models testify to the originality of M. Vinhranovskyi's linguistic thinking, his ability to find unexpected associative connections, revealing an individually modified and rich system of emotional and evaluative meaning plans of somatisms.

Band structures of the bowtie lattice and its ribbons influenced by $$\mathcal{PT}$$-symmetric imaginary potentials

Band structures of the bowtie lattice and its ribbons influenced by $$\mathcal{PT}$$-symmetric imaginary potentials

Effective scattering and Efimov physics in the presence of two-body dissipation

Two-body dissipation usually gives rise to a complex interaction. Here we study the effect of two-body dissipation on few-body physics, including the fundamental two-body effective scattering and the three-body Efimov physics. By employing a two-channel model that incorporates the decay of closed-channel molecules (generating the two-body dissipation), we explicitly relate the real and imaginary part of the inverse scattering length (${a}_{s}^{\ensuremath{-}1}$) to closed-channel detuning and decay rate. In particular, we show that the imaginary part of ${a}_{s}^{\ensuremath{-}1}$ is given by the product of the molecule decay rate and the effective range. Such complex scattering length is found to generate an additional imaginary Coulomb potential when three atoms come close to each other, thereby suppressing the formation of trimer bound states and modifying the conventional discrete scaling in Efimov physics.

Novel vortices and the role of a complex chemical potential in a rotating holographic superfluid

In this work, we have analytically devised novel vortex solutions in a rotating holographic superfluid. To achieve this result, we have considered a static disc at the AdS boundary and let the superfluid rotate relative to it. This idea has been numerically exploited in [1] where formation of vortices in such a setting was reported. We have found that these vortex solutions are eigenfunctions of angular momentum. We have also shown that vortices with higher winding numbers are associated with higher quantized rotation of the superfluid. We have, then, analysed the equation of motion along bulk AdS direction using St\"urm-Liouville eigenvalue approach. A surprising outcome of our study is that the chemical potential must be purely imaginary. We have then observed that the winding number of the vortices decreases with the increase in the imaginary chemical potential. We conclude from this that imaginary chemical potential leads to less dissipation in such holographic superfluids.

Notes on massless scalar field partition functions, modular invariance and Eisenstein series

The partition function of a massless scalar field on a Euclidean spacetime manifold ℝd−1 × \U0001d54b2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝp × \U0001d54bq+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On \U0001d54bd+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density

The hadron resonance gas (HRG) model is often believed to correctly describe the confined phase of QCD. This assumption is the basis of many phenomenological works on QCD thermodynamics and of the analysis of hadron yields in relativistic heavy ion collisions. We use first-principle lattice simulations to calculate corrections to the ideal HRG. Namely, we determine the sub-leading fugacity expansion coefficients of the grand canonical free energy, receiving contributions from processes like kaon-kaon or baryon-baryon scattering. We achieve this goal by performing a two dimensional scan on the imaginary baryon number chemical potential ($\mu_B$) - strangeness chemical potential ($\mu_S$) plane, where the fugacity expansion coefficients become Fourier coefficients. We carry out a continuum limit estimation of these coefficients by performing lattice simulations with temporal extents of $N_\tau=8,10,12$ using the 4stout-improved staggered action. We then use the truncated fugacity expansion to extrapolate ratios of baryon number and strangeness fluctuations and correlations to finite chemical potentials. Evaluating the fugacity expansion along the crossover line, we reproduce the trend seen in the experimental data on net-proton fluctuations by the STAR collaboration.

Topological properties of non-Hermitian Creutz ladders

We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials, and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes. The non-Hermitian skin effect (NHSE), which is known to break the bulk–boundary correspondence (BBC), emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder. The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart, whether with or without the NHSE. In one scenario without the NHSE, the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector. The NHSE itself also possesses some unusual behaviors in this system, including a high spectral winding without the presence of long-range hoppings, and a competition between two types of the NHSE, with the same and opposite inverse localization lengths for the two bands, respectively. Furthermore, it is found that the NHSE in this model does not always break the conventional BBC, which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.

Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density

The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased. In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint. In this article I review recent progress towards an understanding of the nature of the transition in the massless limit, and its critical temperature at zero density. Combined with increasingly detailed studies of the physical crossover region, current data bound a possible critical point to μB ≳ 3T.

A_0-condensation in quark-gluon plasma with finite baryon density

In the present paper, we return to the problem of spontaneous generation of the A_0-background field in QCD at finite temperature and a quark chemical potential, mu . On the lattice, this problem was studied by different approaches where an analytic continuation to the imaginary potential i mu has been used. Here we consider both, real and imaginary chemical potential, analytically within the two-loop gauge-fixing independent effective potential W_{eff.}. We realize the gauge independence in to ways: (1) on the base of Nielsen’s identity and (2) expressing the potential in terms of Polyakov’s loop. Firstly we reproduce the known expressions in terms of Bernoulli’s polynomials for the gluons and quarks. Then, we calculate the mu -dependence, either for small mu as expansion or numerically for finite mu , real and imaginary. One result is that the chemical potential only weakly changes the values of the condensate fields, but quite strongly deepens the minima of the effective potential. We investigate the dependence of Polyakov’s loop in the minimum of the effective potential, thermodynamic pressure and Debye’s mass on the chemical potential. Comparisons with other results are given.

Protected quantum coherence by gain and loss in a noisy quantum kicked rotor

We study the effects of non-Hermiticity on quantum coherence via a noisy quantum kicked rotor (NQKR). The random noise comes from the fluctuations in kick amplitude at each time. The non-Hermitian driving indicates the imaginary kicking potential, representing the environment-induced atom gain and loss. In the absence of gain and loss, the random noise destroys quantum coherence manifesting dynamical localization, which leads to classical diffusion. Interestingly, in the presence of non-Hermitian kicking potential, the occurrence of dynamical localization is highly sensitive to the gain and loss, manifesting the restoration of quantum coherence. Using the inverse participation ratio arguments, we numerically obtain a phase diagram of the classical diffusion and dynamical localization on the parameter plane of noise amplitude and non-Hermitian driving strength. With the help of analysis on the corresponding quasieigenstates, we achieve insight into dynamical localization, and uncover that the origin of the localization is interference between multiple quasi-eigenstates of the quantum kicked rotor. We further propose an experimental scheme to realize the NQKR in a dissipative cold atomic gas, which paves the way for future experimental investigation of an NQKR and its anomalous non-Hermitian properties.

Non-Hermitian Lindhard function and Friedel oscillations

Friedel oscillations are ubiquitous around localized defects in Hermitian quantum mechanics. Here we study their fate around a non-Hermitian, imaginary impurity and evaluate the corresponding non-Hermitian Lindhard function in one dimension, where quantum effects are traditionally enhanced due to spatial confinement. Most importantly, we find that the static limit of the non-Hermitian Lindhard function has no divergence at twice the Fermi wave number and vanishes identically for all other wave numbers at zero temperature. Consequently, no Friedel oscillations are induced by a non-Hermitian, imaginary impurity to lowest order in the impurity potential at zero temperature. Our findings are corroborated numerically on a tight-binding ring by switching on a weak real or imaginary potential. We identify conventional Friedel oscillations or a heavily suppressed density response, respectively.

Non-Hermitian skin effect beyond the tight-binding models

The energy bands of non-Hermitian systems exhibit nontrivial topological features that arise from the complex nature of the energy spectrum. Under periodic boundary conditions (PBCs), the energy spectrum describes rather generally closed loops in complex plane, characterized by integer nonzero winding numbers. Such nontrivial winding provides the topological signature of the non-Hermitian skin effect (NHSE), i.e., the macroscopic condensation of bulk states at the lattice edges under open boundary conditions (OBCs). In spite of the great relevance of band winding in the non-Hermitian topological band theory and the related NHSE, most of current results rely on tight-binding models of non-Hermitian systems, while exact Bloch wave function analysis of the NHSE and related topological band theory is still lacking. While tight-binding models can correctly describe narrow-band electronic states with a relatively weak degree non-Hermiticity, they are not suited to describe high-energy wide-band electronic states and/or regimes corresponding to strong non-Hermiticity. Here we consider the single-particle continuous Schr\"odinger equation in a periodic potential, in which non-Hermiticity is introduced by an imaginary vector potential in the equation, and show that the NHSE is ubiquitous under OBC and characterized by a nonvanishing integer winding number, even though the energy spectrum under PBC always comprises an open curve, corresponding to high-energy electronic states. We also show that the interior of the PBC energy spectrum corresponds to the complex eigenenergies sustaining localized (edge) states under semi-infinite boundary conditions.

Anderson localization induced by complex potential

In the Hermitian regime, uncorrelated disorder potential in one-dimensional lattice induces Anderson localization, whereas quasiperiodic potential can lead to both localized and extended phases, depending on the potential strength. In this study, we investigate the non-Hermitian regime. We analytically and numerically study Anderson localization in a one-dimensional lattice with the non-Hermitian complex disorder and quasiperiodic potential. We present a non-Hermitian Su-Schrieffer-Heeger (SSH) chain and demonstrate that the Hermitian counterpart with full real spectrum is a standard Anderson chain, which indicates that a nonzero imaginary disorder on-site potential can induce standard Anderson localization. We further demonstrate that the non-Hermitian Aubry-André -Harper (AAH) model exhibits a transition in parameter space, which separates the localization and delocalization phases and is determined by the self-duality of the model. This indicates that a pure imaginary quasiperiodic potential plays the same role as a real quasiperiodic potential in the transition point between localization and delocalization. Notably, a system with complex quasiperiodic potential exhibits an interference-like pattern on the transition points, which arises from the interplay between the real and imaginary components.

Effects of the hyperscaling violation and dynamical exponents on the imaginary potential and entropic force of heavy quarkonium via holography

The imaginary potential and entropic force are two important different mechanisms to characterize the dissociation of heavy quarkonia. In this paper, we calculate these two quantities in strongly coupled theories with anisotropic Lifshitz scaling and hyperscaling violation exponent using holographic methods. We study how the results are affected by the hyperscaling violation parameter theta and the dynamical exponent z at finite temperature and chemical potential. Also, we investigate the effect of the chemical potential on these quantities. As a result, we find that both mechanisms show the same results: the thermal width and the dissociation length decrease as the dynamical exponent and chemical potential increase or as the hyperscaling violating parameter decreases.

Reduction of the neutron imaginary potential off the stability line and its possible impact on neutron capture rates

The effect of the isovector imaginary optical potential has been studied experimentally by using the particle-evaporation technique for the $^{11}\mathrm{B}+^{48}\mathrm{Ca}$ reaction with a 21.8 MeV $^{11}\mathrm{B}$ beam. Spectra of neutron, proton, and $\ensuremath{\alpha}$ particles emitted from the neutron-rich compound nucleus $^{59}\mathrm{Mn}$ have been measured and analyzed with traditional optical model potentials with their original parametrizations as well as with adjusted isovector imaginary components. It is shown that the isovector component of the imaginary potential is indispensable in the reproduction of proton and $\ensuremath{\alpha}$-particle yields from this reaction and even needs to be enhanced compared with the suggestions of the original model parametrizations. This can lead to important consequences for astrophysical reaction-rate calculations.