Bosonic Case Research Articles

Bridging the gap between topological non-Hermitian physics and open quantum systems

We relate topological properties of non-Hermitian systems and observables of quantum open systems by using the Keldysh path-integral method. We express Keldysh Green's functions in terms of effective non-Hermitian Hamiltonians that contain all the relevant topological information. We arrive at a frequency dependent topological index that is linked to the response of the system to perturbations at a given frequency. We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases

Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet

Using the ambitwistor string, we complete the list of celestial operator product expansion (OPE) coefficients for supersymmetric theories. This uses the ambitwistor string worldsheet conformal field theory to dynamically generate the OPE coefficients for maximally supersymmetric gauge theory, as well as gravity and Einstein-Yang-Mills theories, including all helicity and orientation configurations. This extends previous purely bosonic results [T. Adamo et al., arXiv:2111.02279] to include supersymmetry and provides explicit formulas which are, to the best of our knowledge, not in the literature. We also examine how the supersymmetric infinite dimensional soft algebras behave compared to the purely bosonic cases.

Regularization of a strong–weak duality between pointlike interactions in one dimension

Pointlike interactions between bosons in 1D are related to pointlike interactions between fermions through the Girardeau mapping. This mapping is a strong–weak duality since the coupling constants in the bosonic and fermionic cases are inversely proportional to each other. We present a regularization of these pointlike interactions that preserves the strong–weak duality, contrary to previously known Hermitian regularizations. This is proven rigorously. This allows one to use this duality perturbatively and we illustrate it in the Lieb–Liniger model at strong coupling.

Dynamical fermionization in a one-dimensional Bose-Fermi mixture

After release from the trap the momentum distribution of an impenetrable gas asymptotically approaches that of a spinless noninteracting Fermi gas in the initial trap. This phenomenon is called dynamical fermionization and, very recently, has been experimentally confirmed in the case of the Lieb-Liniger model in the Tonks-Girardeau regime. We prove analytically and confirm numerically that following the removal of axial confinement the strongly interacting Bose-Fermi mixture exhibits dynamical fermionization and the asymptotical momentum distribution of each component has the same shape as its density profile at $t=0$. Under a sudden change of the trap frequency to a new nonzero value the dynamics of both fermionic and bosonic momentum distributions presents characteristics which are similar to the case of single component bosons experiencing a similar quench. Our results are derived using a product representation for the correlation functions which, in addition to analytical considerations, can be implemented numerically very easily with complexity which scales polynomially in the number of particles.

Mixing particle production for relaxion mechanism

We consider the production of two heavy gauge bosons as a relaxation stopping mechanism. In this work, we analyse the conditions for a tachyonic mode for a linear combination of gauge bosons and show that the criteria are significantly different than the single gauge boson case. Moreover, the implementation of the mechanism on the U(1)′ model is demonstrated. We discuss various constraints for the relaxion mechanism. The phenomenology of the heavy gauge boson is also explored. We finally show a benchmark point of parameter space considering all constraints from relaxion and the U(1)′ mixing sector.

Topological transitions driven by quantum statistics and their electrical circuit emulation

Topological phases exhibit a plethora of striking phenomena, including disorder-robust localization and the propagation of waves of various nature. While this physics is actively explored in bosonic and fermionic cases, the topological phases of anyons --- particles with fractional quantum statistics --- are largely uncharted. Here, we unveil the topological transition mediated by the particles' quantum statistics that arises for two-anyon and three-anyon excitations in a one-dimensional array described by the extended Hubbard model. As we demonstrate, the interplay of two-particle interactions and tunneling processes enables topological edge states of anyon pairs whose existence and localization at one or another edge of the one-dimensional system is governed by the quantum statistics of particles. Since a direct realization of the proposed system is challenging, we develop a rigorous method to emulate the eigenmodes and eigenenergies of anyon pairs with resonant electrical circuits.

Anyons in One Dimension

A fascinating possibility exists for exotic quantum statistics to interpolate between the familiar cases of bosons and fermions: the anyon, observed in two dimensions. But how does it behave in one?

Evolution between quantum Hall and conducting phases: Simple models and some results

Quantum many-particle systems in which the kinetic energy, strong correlations, and band topology are all-important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these elements are present. We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the lowest Landau level (LLL). This is the familiar quantum Hall regime with rich physics determined by particle filling and statistics. A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a Chern band with a finite bandwidth. The states obtained in the quantum Hall regime evolve into conducting states in the limit of large bandwidth. We study this evolution in detail for the specific case of bosons at filling factor $\ensuremath{\nu}=1$. In the quantum Hall regime, the ground state at this filling is a gapped quantum hall state (the ``bosonic Pfaffian''), which may be viewed as descending from a (bosonic) composite Fermi liquid. At large bandwidth, the ground state is a bosonic superfluid. We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite Fermi liquid, we show that the evolution into the superfluid can be usefully described by a noncommutative quantum field theory in a periodic potential.

Planar solutions of higher-spin theory. Nonlinear corrections

Leading order higher-spin corrections to the linearized higher-spin black brane are analyzed in four dimensions. It is shown that the static solution that respects planar symmetry exists in the bosonic case at given order. Its higher-spin Weyl tensors are found in a closed form and are shown to have the double copy origin. The effect of higher-spin fields to form a strictly positive scalar condensate for any values of higher-spin charges is observed.

General relativity from $p$-adic strings

For an arbitrary prime number $p$, we propose an action for bosonic $p$-adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of worldsheet scaling symmetry of the quantum $p$-adic strings, similar to the ordinary bosonic strings case. It turns out that certain $p$-adic automorphic forms are the plane wave modes of the bosonic fields on $p$-adic strings, and that the regularized normalization of these modes on the $p$-adic worldsheet presents peculiar features which reduce part of the computations to familiar setups in quantum field theory, while also exhibiting some new features that make loop diagrams much simpler. Assuming a certain product relation, we also observe that the adelic spectrum of the bosonic string corresponds to the nontrivial zeros of the Riemann Zeta function.

Fermionic and bosonic fluctuation-dissipation theorem from a deformed AdS holographic model at finite temperature and chemical potential

In this work we study fluctuations and dissipation of a string in a deformed anti-de Sitter (AdS) space at finite temperature and density. The deformed AdS space is a charged black hole solution of the Einstein–Maxwell–Dilaton action. In this background we take into account the backreaction on the horizon function from an exponential deformation of the AdS space. From this model we compute the admittance and study the influence of the temperature and the chemical potential on it. We calculate the two-point correlations functions, and the mean square displacement for bosonic and fermionic cases, from which we obtain the short and large time approximations. For the long time, we obtain a sub-diffusive regime sim log t. Combining the results from the admittance and the correlations functions we check the fluctuation-dissipation theorem for bosonic and fermionic systems.

Ultralight dark matter or dark radiation cosmologically produced from infrared dressing

Infrared dressing of bosonic or fermionic heavy particles by a cloud of massless particles to which they couple is studied as a possible production mechanism of ultra light dark matter or dark radiation in a radiation dominated cosmology. We implement an adiabatic expansion valid for wavelengths much smaller than the Hubble radius combined with a non-perturbative and manifestly unitary dynamical resummation method to study the time evolution of an initial single heavy particle state. We find a striking resemblance to the process of particle decay: the initial amplitude of the single particle decays in time, not exponentially but with a power law with anomalous dimension $\propto t^{-\Delta/2}$ featuring a crossover to $t^{-\Delta}$ as the heavy particle becomes non-relativistic in both bosonic and fermionic cases suggesting certain universality. At long time the asymptotic state is an entangled state of the heavy and massless particles. The entanglement entropy is shown to grow under time evolution describing the flow of information from the initial single particle to the final multiparticle state. The expectation value of the energy momentum tensor in the asymptotic state is described by two indpendent fluids each obeying covariant conservation, one of heavy particles and the other of relativistic (massless) particles (dark radiation). Both fluids share the same frozen distribution function and entropy as a consequence of entanglement.

Scattering hypervolume of spin-polarized fermions

We analyze the collision of three identical spin-polarized fermions at zero collision energy, assuming arbitrary finite-range potentials, and define the corresponding three-body scattering hypervolume ${D}_{F}$. The scattering hypervolume $D$ was first defined for identical bosons in 2008. It is the three-body analog of the two-body scattering length. We solve the three-body Schr\"odinger equation asymptotically when the three fermions are far apart or one pair and the third fermion are far apart, deriving two asymptotic expansions of the wave function. Unlike the case of bosons for which $D$ has the dimension of length to the fourth power, here the ${D}_{F}$ we define has the dimension of length to the eighth power. We then analyze the interaction energy of three such fermions with momenta $\ensuremath{\hbar}{\mathbf{k}}_{1}$, $\ensuremath{\hbar}{\mathbf{k}}_{2}$, and $\ensuremath{\hbar}{\mathbf{k}}_{3}$ in a large periodic cubic box. The energy shift due to ${D}_{F}$ is proportional to ${D}_{F}/{\mathrm{\ensuremath{\Omega}}}^{2}$, where $\mathrm{\ensuremath{\Omega}}$ is the volume of the box. We also calculate the shifts of energy and pressure of spin-polarized Fermi gases due to a nonzero ${D}_{F}$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases at finite temperatures.

Entropy Minimization for Many-Body Quantum Systems

The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their work is that of local quantum Gibbs states, which are quantum statistical equilibria with prescribed particle, current, and energy densities at each point of space (here R d , d $\ge$ 1). They assume that such local Gibbs states exist, and show that if the quantum system is initially in a local Gibbs state, then the system stays, in an appropriate asymptotic limit, in a Gibbs state with particle, current, and energy densities now solutions to the Euler equations. Our main contribution in this work is to prove that such local quantum Gibbs states can be constructed from prescribed densities under mild hypotheses, in both the fermionic and bosonic cases. The problem consists in minimizing the von Neumann entropy in the quantum grand canonical picture under constraints of local particle, current, and energy densities. The main mathematical difficulty is the lack of compactness of the minimizing sequences to pass to the limit in the constraints. The issue is solved by defining auxiliary constrained optimization problems, and by using some monotonicity properties of equilibrium entropies.

A shell of bosons in spherically symmetric spacetimes

The thermodynamic properties of a shell of bosons with the inner surface locating at Planck length away from the horizon of Schwarzschild black holes by using statistical mechanics are studied. The covariant partition function of bosons is obtained, from which the Bose-Einstein condensation of bosons is found at a non-zero temperature in the curved spacetimes. As a special case of bosons, we analyze the entropy of photon gas near the horizon of the Schwarzschild black hole, which shows an area dependence similar to the Bekenstein-Hawking entropy. The results may offer new perspectives on the study of black hole thermodynamics. All these are extended to the D+1 dimensional spherically symmetric static spacetimes.

Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization

We investigate the interactions of discrete zero-form and one-form global symmetries in (1+1)d theories. Focus is put on the interactions that the symmetries can have on each other, which in this low dimension result in 2-group symmetries or symmetry fractionalization. A large part of the discussion will be to understand a major feature in (1+1)d: the multiple sectors into which a theory decomposes. We perform gauging of the one-form symmetry, and remark on the effects this has on our theories, especially in the case when there is a global 2-group symmetry. We also implement the spectral sequence to calculate anomalies for the 2-group theories and symmetry fractionalized theory in the bosonic and fermionic cases. Lastly, we discuss topological manipulations on the operators which implement the symmetries, and draw insights on the (1+1)d effects of such manipulations by coupling to a bulk (2+1)d theory.

Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

The recently proposed map [5] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [1] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial (t=0) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times t<0t<0. A similar singularity appears at t = T/4t=T/4, where T is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at t > T/4t>T/4. Here, we first map—using the scale invariance of the problem—the trapped motion to an untrapped one. Then we show that in the new representation, the solution [5] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [7]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers’ equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the t=0 singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [9]. At t=T/8t=T/8, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [5] and the Damski-Chandrasekhar shock wave becomes invalid.

The specificity of the interactions of electroweak gauge bosons coming from extra dimensions

We discuss the specificity of the interactions of the electroweak gauge boson excitations in models with warped extra dimensions and the Standard Model fields living in the bulk. In particular, we show that the couplings of the gauge boson excitations [Formula: see text], [Formula: see text], and [Formula: see text] to the SM gauge bosons treated as the zero modes of the 5D gauge fields are either exactly equal to zero or very much suppressed. In the former case, the three-particle and four-particle interaction Lagrangians of the SM gauge bosons and their lowest excitations are found explicitly. Meanwhile, the couplings of [Formula: see text], [Formula: see text], and [Formula: see text] to the SM fermions are nonzero allowing for their production and decays. These are the characteristic features of the gauge boson excitations in models with warped extra dimensions, which distinguish them from the gauge boson excitations in other models beyond the SM.

Relativistic Borromean states * *Supported by the National Natural Science Foundation of China (11875002, 11804376), Postdoctoral Innovative Talent Support Program of China (BX20190180). Also supported by the Zhuobai Program of Beihang University

In this work, the existence of Borromean states is discussed for bosonic and fermionic cases in both the relativistic and non-relativistic limits from the 3-momentum shell renormalization. With the linear bosonic model, we check the existence of Efimov-like states in the bosonic system. In both limits a geometric series of singularities is found in the 3-boson interaction vertex, while the energy ratio is reduced by around 70% in the relativistic limit because of the anti-particle contribution. Motivated by the quark-diquark model in heavy baryon studies, we have carefully examined the p-wave quark-diquark interaction and found an isolated Borromean pole at finite energy scale. This may indicate a special baryonic state of light quarks in high energy quark matter. In other cases, trivial results are obtained as expected. In the relativistic limit, for both bosonic and fermionic cases, potential Borromean states are independent of the mass, which means the results would also be valid even in the zero-mass limit.

Confinement of bosonic and spinning particles in braneworlds

In this paper the confinement of bosonic and spinning test particles in smooth Randall-Sundrum models is studied. For this, we show the possibility of finding an effective potential that describes the motion of the particle over the extra dimension. For the bosonic case, it is a known fact that free test particles can be located neither on thin nor on thick branes. Recently, a coupling to a scalar field has been used to localize a limited range of masses. Up to now, no trapped test particles of any mass over the brane were found. In order to solve this, it is shown that a coupling with the dilaton may trap particles of any mass. Next, the spinning particle is analyzed. The spin variables, , introduced an interaction with the Riemann curvature tensor. It introduced a correction to the effective potential. By analyzing it, it was found that the spinning particle may be localized at a different position from the one of the brane. It is also shown that a spinning particle over the brane may escape to infinity. Therefore, it is concluded that free bosonic and spinning particles are not trapped in the brane.