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This paper explores a novel revision of the Faddeev equation for three-body (3B) bound states, as initially proposed in Ref. [J. Golak, K. Topolnicki, R. Skibiński, W. Glöckle, H. Kamada, A. Nogga, Few Body Syst. 54 , 2427 (2013)]. This innovative approach, referred to as t- matrix-free in this paper, directly incorporates two-body (2B) interactions and completely avoids the 2B transition matrices. We extend this formalism to relativistic 3B bound states using a three-dimensional (3D) approach without using partial wave decomposition. To validate the proposed formulation, we perform a numerical study using spin-independent Malfliet–Tjon and Yamaguchi interactions. Our results demonstrate that the relativistic t- matrix-free Faddeev equation, which directly implements boosted interactions, accurately reproduces the 3B mass eigenvalues obtained from the conventional form of the Faddeev equation, referred to as t- matrix-dependent in this paper, with boosted 2B t -matrices. Moreover, the proposed formulation provides a simpler alternative to the standard approach, avoiding the computational complexity of calculating boosted 2B t -matrices and leading to significant computational time savings. [ABSTRACT FROM AUTHOR]

Polarons, quasiparticles resulting from the interaction between an impurity and the collective excitations of a medium, play a fundamental role in physics, mainly because they represent an essential building block for understanding more complex many-body phenomena. In this manuscript, we study the spectral properties of a single impurity mixed with identical bosons in a one-dimensional lattice with power-law hopping. In particular, based on the so-called T-matrix approximation, we show the existence of well-defined quasiparticle branches for several tunneling ranges and for both repulsive and attractive impurity-boson interactions. Furthermore, we demonstrate the persistence of the attractive polaron branch when the impurity-boson bound state is absorbed into the two-body continuum and that the attractive polaron becomes more robust as the range of the hopping increases. The results discussed here are relevant for the understanding of the equilibrium properties of quantum systems with power-law interactions. [ABSTRACT FROM AUTHOR]

We present the generalized optical theorem and its applications with special emphasis on the roles of bound states. First, we prove the theorem which gives a necessary and sufficient condition for a function |$\langle {\boldsymbol {k}}^{\prime } | T | {\boldsymbol {k}} \rangle$| of two variables |${\boldsymbol {k}}^{\prime }$| and |${\boldsymbol {k}}$| to be physically acceptable as a half-on-shell T-matrix, i.e., to have an underlying Hermitian potential V. Secondly, using the theorem, we construct a scattering theory starting from a physically acceptable half-on-shell T-matrix |$\langle {\boldsymbol {k}}^{\prime } | T | {\boldsymbol {k}} \rangle$|⁠ , which in turn introduces a very useful classification scheme of Hermitian potentials. In the end, as an application of our theory, we present the most general solution of the inverse scattering problem with numerical examples. [ABSTRACT FROM AUTHOR]

We discuss the hadron–quark crossover accompanied by the formation of Cooper triples (three-body counterpart of Cooper pairs) by analogy with the Bose–Einstein condensate to Bardeen–Cooper–Schrieffer crossover in two-component fermionic systems. Such a crossover is different from a phase transition, which often involves symmetry breaking. We calculate the in-medium three-body energy from the three-body T-matrix with a phenomenological three-body force characterizing a bound hadronic state in vacuum. With increasing density, the hadronic bound-state pole smoothly undergoes a crossover toward the Cooper triple phase where the in-medium three-body clusters coexist with the quark Fermi sea. The relation to the quarkyonic matter model can also be found in a natural manner. [ABSTRACT FROM AUTHOR]

Magnetic superconductors define a broad class of strongly correlated materials in which superconductivity may coexist with either localized or itinerant long-range magnetic order. In this work we consider a multiband model of a disordered magnetic superconductor which realizes coexistence of unconventional superconductivity and a spin-density-wave. We derive an exact T -matrix and compute a single particle density of states in this system. In a purely superconducting state the interband scattering potential leads to an appearance of the localized Yu–Shiba–Rusinov bound states. Our main finding is that in the fairly broad swath of the coexistence region superconductivity remains fully gapped despite the presence of the impurity bands. We also discuss the effects of spatial inhomogeneities on the density of states in strongly contaminated superconductors. • Superconductivity may coexist with spin-density-wave order in multiband metals. • Long-range disorder widens coexistence region of the phase diagram. • Strong impurities lead to appearance of localized sub-gap states and narrow bands. • The threshold energy to break Cooper pairs remains finite in the coexistence phase. • Fluctuations cause smearing of the sharp gap edges resulting in the tail states. [ABSTRACT FROM AUTHOR]

The strongly coupled phase of the quark-gluon plasma (QGP) is studied here by resorting to a T-matrix formulation in which the medium is seen as a nonideal gas of quasiparticles (quarks, antiquarks, and gluons) interacting nonpertubatively. In the temperature range under study, (1-5)Tc, where Tc is the temperature of deconfinement, the interactions are expected to be strong enough to generate bound states. The dissociation temperature of such binary bound states is thus computed here. The more the quasiparticles involved in the binary system are heavy, the more the bound state is likely to survive significantly above Tc. Then the QGP equations of state at zero and small baryonic potential are computed for Nf = 2 and Nf = 2 + 1 by resorting to the Dashen, Ma, and Bernstein formulation of statistical mechanics. Comparisons with current lattice QCD data are presented. [ABSTRACT FROM AUTHOR]

• Self-consistent T-matrix approach is adapted for quantum magnets with bond disorder. • Density of states and gap described in both resonant and non-resonant regimes. • Theory successfully applied for experimental data on Ba (3 - x) Sr x Cr 2 O 8 . The analytical theory of density of states (DOS) in three-dimensional quantum magnets with the bond disorder is proposed based on the self-consistent T-matrix approximation (SCTMA). It successfully describes the DOS both for resonant and non-resonant scattering, whose emergence is governed by the ratio of scattering length and the average distance between impurities, which concentration is denoted as c. Corrections to the quasiparticle band gap in these cases are shown to scale as c 2 / 3 and c , respectively. Moreover, the theory yields a semi-circle form of the DOS for the bound states inside the gap, which results in highly nontrivial DOS in the intermediate parameter region between the two limiting cases when the band DOS and the semi-circle overlap. Long-wavelength excitations are discussed. In the resonant regime their damping scales as c 2 / 3 , which, according to Ioffe-Regel criterion, corresponds to their localization. Applicability of the theory is illustrated by its quantitative agreement with the recent experimental data on spin-dimer system Ba 3− x Sr x Cr 2 O 8. [ABSTRACT FROM AUTHOR]

We consider a superconductor proximity coupled to a two-dimensional ferromagnetic film with a skyrmion texture. Using the T-matrix calculations and numerical modeling we calculate the spin-polarized local density of states in the superconductor in the vicinity of the skyrmion. We predict the skyrmion bound states that are induced in the superconductor, similar to the well-known Yu-Shiba-Rusinov states. The bound-state wave functions have spatial power-law decay. It is suggested that superconductivity could facilitate an effective long-range interaction between skyrmions when bound-state wave functions overlap. [ABSTRACT FROM AUTHOR]