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In an attempt to better leverage superconducting quantum computers, scaling efforts have become the central concern. These efforts have been further exacerbated by the increased complexity of these circuits. The added complexity can…
Quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single qubit and two qubits quantum logic ports. We…
A multi-band effective-mass Hamiltonian is derived for lattice-matched semiconductor nanostructures in a slowly varying external magnetic field. The theory is derived from the first-principles magnetic-field coupling Hamiltonian of Pickard…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
We derive effective Floquet Hamiltonians for twisted bilayer graphene driven by circularly polarized light in two different regimes beyond the weak-drive, high frequency regime. First, we consider a driving protocol relevant for experiments…
Starting from a general $N$-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows…
We express discrete Painlev\'e equations as discrete Hamiltonian systems. The discrete Hamiltonian systems here mean the canonical transformations defined by generating functions. Our construction relies on the classification of the…
Motivated by recent studies on topologically non-trivial moir\'{e} bands in twisted bilayer transition metal dichalcogenides (TMDs), we study MoTe$_2$ bilayer systems subject to pressure, which is applied perpendicular to the material…
We derive an effective Hamiltonian that describes a cross-Kerr type interaction in a system involving a two-level trapped ion coupled to the quantized field inside a cavity. We assume a large detuning between the ion and field (dispersive…
We propose an adiabatic-elimination formalism in the dispersive regime based on a transition-centric perturbation theory. The perturbative expansion is recast into a diagrammatic framework, while adiabatic elimination is implemented through…
We consider a quantum system linearly coupled to a reservoir of harmonic oscillators. For finite coupling strengths, the stationary distribution of the damped system is not of the Gibbs form, in contrast to standard thermodynamics. With the…
We show that a large class of dissipative systems can be brought to a canonical form by introducing complex co-ordinates in phase space and a complex-valued hamiltonian. A naive canonical quantization of these systems lead to non-hermitean…
We show how to derive fixed-point Hamiltonians in quantum mechanics from a proposed renormalization group invariance approach that relies in a subtraction procedure at a given energy scale. The scheme is valid for arbitrary interactions…
We propose the concept of `topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of topological Hamiltonian are significantly different from the physical energy spectra, but we show…
The present paper reviews recent achievements on the ab initio determination of effective model Hamiltonians aimed at the description of strongly correlated materials. These models (Heisenberg, $t-J$, extended Hubbard, Kondo, etc) are…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…
Collective spins of large atomic samples trapped inside optical resonators can carry quantum information that can be processed in a way similar to quantum computation with continuous variables. It is shown here that by combining the…
Solutions to explicit time-dependent problems in quantum mechanics are rare. In fact, all known solutions are coupled to specific properties of the Hamiltonian and may be divided into two categories: One class consists of time-dependent…
We propose a scheme to engineer an effective spin Hamiltonian starting from a system of electrons confined in micro-Penning traps. By means of appropriate sequences of electromagnetic pulses, alternated to periods of free evolution, we…
In this short review we describe the process of designing a superconducting circuit device for quantum information applications. We discuss the factors that must be considered to implement a desired effective Hamiltonian on a device. We…