Quantum-classical correspondence of a system of interacting bosons in a triple-well potential

We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science. In the integrable limits, our analysis of the stationary points of the semiclassical Hamiltonian reveals critical points associated with second-order quantum phase transitions. In the nonintegrable domain, the system exhibits crossovers. Depending on the parameters and quantities, the quantum-classical correspondence holds for very few bosons. In some parameter regions, the ground state is robust (highly sensitive) to changes in the interaction strength (tilt amplitude), which may be of use for quantum information protocols (quantum sensing).

Mildly flavoring domain walls in Sp(N) SQCD

We consider supersymmetric domain walls of four-dimensional $$ \mathcal{N} $$ N = 1 Sp(N) SQCD with F = N + 1 and F = N + 2 flavors.First, we study numerically the differential equations defining the walls, classifying the solutions. When F = N + 2, in the special case of the parity-invariant walls, the naive analysis does not provide all the expected solutions. We show that an infinitesimal deformation of the differential equations sheds some light on this issue.Second, we discuss the 3d$$ \mathcal{N} $$ N = 1 Chern-Simons-matter theories that should describe the effective dynamics on the walls. These proposals pass various tests, including dualities and matching of the vacua of the massive 3d theory with the 4d analysis. However, for F = N +2, the semiclassical analysis of the vacua is only partially successful, suggesting that yet-to-be-understood strong coupling phenomena are into play in our 3d$$ \mathcal{N} $$ N = 1 gauge theories.

Airy Structures for Semisimple Lie Algebras

We give a complete classification of Airy structures for finite-dimensional simple Lie algebras over $${\mathbb {C}}$$ C , and to some extent also over $${\mathbb {R}}$$ R , up to isomorphisms and gauge transformations. The result is that the only algebras of this type which admit any Airy structures are $$\mathfrak {sl}_2$$ sl 2 , $$\mathfrak {sp}_4$$ sp 4 and $$\mathfrak {sp}_{10}$$ sp 10 . Among these, each admits exactly two non-equivalent Airy structures. Our methods apply directly also to semisimple Lie algebras. In this case it turns out that the number of non-equivalent Airy structures is countably infinite. We have derived a number of interesting properties of these Airy structures and constructed many examples. Techniques used to derive our results may be described, broadly speaking, as an application of representation theory in semiclassical analysis.

Semiclassical analysis of the tensor power spectrum in the Starobinsky inflationary model

In this work, we calculate the tensor power spectrum and the tensor-to-scalar ratio [Formula: see text] within the frame of the Starobinsky inflationary model using the improved uniform approximation method and the third-order phase-integral method. We compare our results with those obtained with numerical integration and the slow-roll approximation to second-order. We have obtained consistent values of [Formula: see text] using the different approximations, and [Formula: see text] is inside the interval reported by observations.

Classical and quantum $$(2+1)$$-dimensional spatially homogeneous string cosmology

We introduce three families of classical and quantum solutions to the leading order of string effective action on spatially homogeneous $$(2+1)$$ ( 2 + 1 ) -dimensional space-times with the sources given by the contributions of dilaton, antisymmetric gauge B-field, and central charge deficit term $$\varLambda $$ Λ . At the quantum level, solutions of Wheeler–DeWitt equations have been enriched by considering the quantum versions of the classical conditional symmetry equations. Concerning the possible applications of the obtained solutions, the semiclassical analysis of Bohm’s mechanics has been performed to demonstrate the possibility of avoiding the classical singularities at the quantum level.

High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph

The Kubo–Martin–Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and Verboven, proposed an analogue to the KMS condition for infinite classical mechanical systems and highlighted its relationship with the Kirkwood–Salzburg equations and with the Gibbs equilibrium measures. In this paper, we prove that in a certain limiting regime of high temperature the classical KMS condition can be derived from the quantum condition in the simple case of the Bose–Hubbard dynamical system on a finite graph. The main ingredients of the proof are Golden–Thompson inequality, Bogoliubov inequality and semiclassical analysis.