Acta Polytechnica
http://hdl.handle.net/10467/20071
2022-12-07T03:47:57ZHow to understand the structure of beta functions in six-derivative Quantum Gravity?
http://hdl.handle.net/10467/100638
How to understand the structure of beta functions in six-derivative Quantum Gravity?
Rachwał, Lesław
We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical structure of the exact on the full quantum level beta functions obtained previously for three couplings in front of generally covariant terms with four derivatives (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet scalar) in minimal six-derivative quantum gravity in d = 4 spacetime dimensions. The fundamental role here is played by the ratio x of the coupling in front of the term with Weyl tensors to the coupling in front of the term with Ricci scalars in the original action. We draw a relation between the polynomial dependence on x and the absence/presence of enhanced conformal symmetry and renormalizability in the models where formally x → +∞ in the case of four- and six-derivative theories respectively.
2022-01-01T00:00:00ZAnalytic and Algebraic Methods in Physics
http://hdl.handle.net/10467/100637
Analytic and Algebraic Methods in Physics
Khrabustovskii , Andrii; Znojil , Miloslav
null
2022-01-01T00:00:00ZConserved quantities in non-hermitian systems via vectorization method
http://hdl.handle.net/10467/100636
Conserved quantities in non-hermitian systems via vectorization method
Agarwal, Kaustubh S.; Muldoon, Jacob; Joglekar, Yogesh N.
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to characterize and derive conserved quantities, or intertwining operators, in such open systems. As a consequence, we also obtain non-Hermitian or Hermitian operators whose expectations values show single exponential time dependence. By using a simple example of a PT-symmetric dimer that arises in two distinct physical realizations, we demonstrate our procedure for static Hamiltonians and generalize it to time-periodic (Floquet) cases where intertwining operators are stroboscopically conserved. Inspired by the Lindblad density matrix equation, our approach provides a useful additionto the well-established methods for characterizing time-invariants in non-Hermitian systems.
2022-01-01T00:00:00ZRational extension of many particle systems
http://hdl.handle.net/10467/100635
Rational extension of many particle systems
Mandal, Bhabani Prasad
In this talk, we briefly review the rational extension of many particle systems, and is based on a couple of our recent works. In the first model, the rational extension of the truncated Calogero-Sutherland (TCS) model is discussed analytically. The spectrum is isospectral to the original system and the eigenfunctions are completely expressed in terms of exceptional orthogonal polynomials (EOPs). In the second model, we discuss the rational extension of a quasi exactly solvable (QES) N-particle Calogero model with harmonic confining interaction. New long-range interaction to the rational Calogero model is included to construct this QES many particle system using the technique of supersymmetric quantum mechanics (SUSYQM). Under a specific condition, infinite number of bound states are obtained for this system, and corresponding bound state wave functions are written in terms of EOPs.
2022-01-01T00:00:00Z