Related papers: Deformed Richardson-Gaudin model
Hamiltonian Mechanics works for conserved systems and Quantum Mechanics is given in Hamiltonian language. It is considered that complexifying the quantum Hamiltonian, a balanced loss and gain model can be created. The usual mathematics of…
We study the dynamics of the Gaudin magnet ("central-spin model") using machine-learning methods. This model is of practical importance, e.g., for studying non-Markovian decoherence dynamics of a central spin interacting with a large bath…
In this paper, time-independent Hamiltonian systems are investigated via a Lie-group/algebra formalism. The (unknown) solution linked with the Hamiltonian is considered to be a Lie-group transformation of the initial data, where the group…
Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the more general q deformations but with…
We consider $\rm R$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\hat{\mathfrak{g}}=A^{(1)}_{N-1}$, $B^{(1)}_n$, $C^{(1)}_n$,…
The success of the identification of the planar dilatation operator of N=4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been…
The $S$-matrix formulation indicates that a consistent embedding of de Sitter state in quantum gravity is possible exclusively as an excited quantum state constructed on top of a valid $S$-matrix vacuum such as Minkowski. In the present…
Many tight frames of interest are constructed via their Gramian matrix (which determines the frame up to unitary equivalence). Given such a Gramian, it can be determined whether or not the tight frame is projective group frame, i.e., is the…
A $\gamma$-deformed version of $\mathfrak{su}(2)$ algebra has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. Fusion of Jordan-Schwinger realization of complexified $\mathfrak{su}(2)$ with Dyson-Maleev representation…
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…
We consider the trigonometric classical $r$-matrix for $\mathfrak{gl}_N$ and the associated quantum Gaudin model. We produce higher Hamiltonians in an explicit form by applying the limit $q\to 1$ to elements of the Bethe subalgebra for the…
Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy $\Sigma$ of any interacting system, provided one can evaluate the interaction vertex $\Gamma$ exactly. This is however…
We develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. Specifically, we present a geometric formalism that significantly simplifies qudit pulse sequence design, while…
We consider a string on a Jordanian deformation of the $AdS_5\times S^5$ spacetime. This model belongs to the larger class of Homogeneous Yang-Baxter deformations, which preserve classical integrability in the sense that one can construct…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…
Recent works have shown that generic local Hamiltonians can be efficiently inferred from local measurements performed on their eigenstates or thermal states. Realistic quantum systems are often affected by dissipation and decoherence due to…
A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard diagram associated to a given cell complex. In the root-of-unity case, the construction is carried out with a…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…