Related papers: Hierarchy of Spin Operators, Quantum Gates, Entang…
A description of eigensubspaces of the cosine and sine operators is presented. The spectrum of each of these two operator consists of two eigenvalues (1,\,-1) and their eigensubspaces are infinite--dimensional. There are many possible bases…
We study the behavior of the spectrum of the Dirac operator on collapsing S^1-bundles. Convergent eigenvalues will exist if and only if the spin structure is projectable.
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing…
In this article, we prove that the completeness of the Hamilton flow and essential self-adjointness are equivalent for real principal type operators on the circle. Moreover, we study spectral properties of these operators. The proof is…
We revisit conformal quantum mechanics (CQM) from the perspective of sine-square deformation (SSD) and the entanglement Hamiltonian. The operators that correspond to SSD and the entanglement Hamiltonian are identified. Thus, the nature of…
A model operator $H$ associated to a system of three-particles on the three dimensional lattice $\Z^3$ and interacting via pair non-local potentials is studied. The following results are proven: (i) the operator $H$ has infinitely many…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
We show that every Hankel operator $H$ is unitarily equivalent to a pseudo-differential operator $A$ of a special structure acting in the space $L^2 ({\Bbb R}) $. As an example, we consider integral operators $H$ in the space $L^2 ({\Bbb…
We outline the nonlinear transformation in the path integral representation for partition function of O(N) symmetric oscillator systems bringing their duality to certain one-dimensional oscillators with unstable potential shapes. This…
Operators that are associated with several important quantities, like angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into…
Physical systems representing qubits typically have one or more accessible quantum states in addition to the two states that encode the qubit. We demonstrate that active involvement of such auxiliary states can be beneficial in constructing…
The concept of entangled quantum states is considered in the context of systems of identical particles, based on the requirement that in order to represent physical states both for the overall system and the sub-systems which may be…
We consider quantum correlations in a spin-1/2 open chain of $N$ nodes with the XY Hamiltonian using different bases for the density matrix representation and the initial state with a single polarized node. These bases of our choice are…
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) exchange interaction with uniform and non-uniform coupling constants. We show that for an odd number of sites a spin…
We characterize the spectrum and essential spectrum of "essentially linear fractional" composition operators acting on the Hardy space H-two of the open unit disc U. When the symbols of these composition operators have Denjoy-Wolff point on…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can…
Quantum entanglement plays a crucial role not only in understanding Hermitian many-body systems but also in offering valuable insights into non-Hermitian quantum systems. In this paper, we analytically investigate the entanglement…
Spins in gate-defined silicon quantum dots are promising candidates for implementing large-scale quantum computing. To read the spin state of these qubits, the mechanism that has provided the highest fidelity is spin-to-charge conversion…