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Canonical transformation
About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.
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TL;DR: In this article, a one-parameter family of algebras FIO ( Ξ, s ), 0 ⩽ s⩽ ∞, consisting of Fourier integral operators is constructed, which is defined by the decay properties of an associated Gabor matrix around the graph of the canonical transformation.
77 citations
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TL;DR: Ryabinkin et al. as mentioned in this paper proposed an iterative version of the qubit coupled cluster (QCC) method, which employs constant-size quantum circuits at the expense of increasing the Hamiltonian size.
Abstract: An iterative version of the qubit coupled cluster (QCC) method [I.G. Ryabinkin et al., J. Chem. Theory Comput. 14, 6317 (2019)] is proposed. The new method seeks to find ground electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices. Each iteration involves a canonical transformation of the Hamiltonian and employs constant-size quantum circuits at the expense of increasing the Hamiltonian size. We numerically studied the convergence of the method on ground-state calculations for LiH, H$_2$O, and N$_2$ molecules and found that the exact ground-state energies can be systematically approached only if the generators of the QCC ansatz are sampled from a specific set of operators. We report an algorithm for constructing this set that scales linearly with the size of a Hamiltonian.
77 citations
TL;DR: The Hamiltonian formulation of a plasma four-field fluid model that describes collisionless reconnection is presented in this article, which is noncanonical with a corresponding Lie-Poisson bracket.
Abstract: The Hamiltonian formulation of a plasma four-field fluid model that describes collisionless reconnection is presented. The formulation is noncanonical with a corresponding Lie‐Poisson bracket. The bracket is used to obtain new independent families of invariants, so-called Casimir invariants, three of which are directly related to Lagrangian invariants of the system. The Casimirs are used to obtain a variational principle for equilibrium equations that generalize the Grad‐Shafranov equation to include flow. Dipole and homogeneous equilibria are constructed. The linear dynamics of the latter is treated in detail in a Hamiltonian context: canonically conjugate variables are obtained; the dispersion relation is analyzed and exact thresholds for spectral stability are obtained; the canonical transformation to normal form is described; an unambiguous definition of negative energy modes is given; and thresholdssufficientforenergy-Casimirstabilityareobtained. TheHamiltonian formulationisalsousedtoobtainanexpressionforthecollisionlessconductivity and it is further used to describe the linear growth and nonlinear saturation of the collisionless tearing mode. (Some figures in this article are in colour only in the electronic version)
77 citations
TL;DR: In this paper, the matrix elements of the multipole operators between single-particle states in a three-dimensional oscillator potential were derived by applying the Wigner-Eckart theorem with respect to both the Sp(2) and O(3) groups.
Abstract: We use the ideas on linear canonical transformations developed previously to calculate the matrix elements of the multipole operators between single‐particle states in a three‐dimensional oscillator potential. We characterize first the oscillator states in the chain of groups Sp(6)⊃Sp(2)×O(3), Sp(2)⊃OS(2), and O(3)⊃OL(2), and then expand the multipole operators in terms of irreducible tensors with respect to the Sp(2)×O(3) group. Their matrix elements are obtained by applying the Wigner‐Eckart theorem with respect to both the Sp(2) and O(3) groups. In this way an explicit expression for the radial integral of rk, k > 0, is obtained.
77 citations
TL;DR: In this article, the authors proposed a perturbative method for dealing with quantum fluctuations around the type of classical solution which received much attention recently, and they showed that, by going to a moving frame, we can always reduce to perturbation around a time independent classical solution, which is then analogous to the one soliton case.
77 citations