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Publications (18)
In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a canonical transformation which can map the anisotropic oscillator to a corresponding isotropic one. Following this...
In this paper, we discuss some results on integrable Hamiltonian systems with two coordinate variables. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a canonical transformation which can map the anisotropic oscillator to a corresponding isotropic one. Following th...
Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle num...
The Swanson oscillator forms a prototypical example of a $\mathcal{PT}$-symmetric and non-Hermitian system with a quadratic Hamiltonian. The system is described by the generic quadratic Hamiltonian $\hat{H}_{\rm Swanson} = \hbar \Omega_0 \big( \hat{a}^\dagger \hat{a} + \frac{1}{2}\big) + \alpha \hat{a}^2 + \beta ({\hat{a}^\dagger})^2$, where $\Omeg...
In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical counterpart to commutators and anticommutators. In one dimension, i.e., in the presence of one bosonic and one fermioni...
In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., H = H 1 + H 2 , where H 1 and H 2 are the Hamiltonians of two one-dimensional unit-mass oscillators. It is shown that there exist...
Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with $n$-qubit generalisations of Yang-Baxter gates called $n$-simplex operators. Such multi-qubit gates potentially lead to shallower and more efficient quantum circuits as well. Findi...
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less noisy. These are realized through Yang-Baxter or 2-simplex operators. A natural question is to extend this const...
Motivated by the structure of the Swanson oscillator, which is a well-known example of a non-hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators, together with bilinear-coupling terms that do not conserve particle n...
We investigate the phenomenon of disorder-free localization in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation-symmetric many-fermion Hamiltonians and interpret them as generators of continuous-time quantum walks. When the number of fermions is very large we find that all the...
It is well known that the Hamiltonian an $n$-dimensional isotropic oscillator admits of an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle. We introduce a novel set of canonical transformations that map an $n$-dimensional anisotropic oscillator to th...
We investigate localisation in a quantum system with a global permutation symmetry and a superselected symmetry. We start with a systematic construction of many-fermion Hamiltonians with a global permutation symmetry using the conjugacy classes of the permutation group $S_N$, with $N$ being the total number of fermions. The resulting Hamiltonians a...
The fusion basis of Fibonacci anyons supports unitary braid representations that can be utilized for universal quantum computation. We show a mapping between the fusion basis of three Fibonacci anyons, $\{|1\rangle, |\tau\rangle\}$, and the two length 4 Dyck paths via an isomorphism between the two dimensional braid group representations on the fus...
In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit mass oscillators admitting a separable Hamiltonian description, i.e. $H = H_1 + H_2$, where $H_1$ and $H_2$ are the Hamiltonians of two one-dimensional unit mass oscillators, and subsequently show th...
In a (2+1)-dimensional Maxwell–Chern–Simons theory coupled with a fermion and a scalar, which has 𝒩=2 SUSY in the absence of the boundary, supersymmetry is broken on the insertion of a spatial boundary. We show that only a subset of the boundary conditions allowed by the self-adjointness of the Hamiltonian can preserve partial (𝒩=1) supersymmetry,...
It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits of an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle. We introduce a novel set of canonical transformations that map an $n$-dimensional anisotropic oscillator to...
In this note, we study some classical aspects of supersymmetric oscillators, in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket, which emerges as a classical counterpart to commutators and anticommutators from supersymmetric quantum mechanics. In one dimension, i.e. in presence of one bosonic and one f...
In a $(2+1)$-dimensional Maxwell-Chern-Simon theory coupled with a fermion and a scalar, which has $\mathcal{N}=2$ SUSY in absence of the boundary, the insertion of a spatial boundary breaks the supersymmetry. We show that only a subset of the boundary conditions allowed by the self-adjointness of the Hamiltonian can preserve partial $\mathcal{N}=1...
