Effective Hamiltonian Formalism Research Articles

Calculation of quasi-diabatic states within the DFT/MRCI(2) framework: The QD-DFT/MRCI(2) method.

We describe a procedure for the calculation of quasi-diabatic states within the recently introduced DFT/MRCI(2) framework [S. P. Neville and M. S. Schuurman, J. Chem. Phys. 157, 164103 (2022)]. Based on an effective Hamiltonian formalism, the proposed procedure, which we term QD-DFT/MRCI(2), has the advantageous characteristics of being simultaneously highly efficient and effectively black box in nature while directly yielding both quasi-diabatic potentials and wave functions of high quality. The accuracy and efficiency of the QD-DFT/MRCI(2) formalism are demonstrated via the simulation of the vibronic absorption spectra of furan and chlorophyll a.

Quantum coherent control in pulsed waveguide optomechanics

Coherent control of traveling acoustic excitations in a waveguide system is an interesting way to manipulate and transduce classical and quantum information. So far, these interactions, often based on optomechanical resonators or Brillouin scattering, have been studied in the steady-state regime using continuous waves. However, waveguide experiments are often based on optical pump pulses, which require treatment in a dynamic framework. In this paper, we present an effective Hamiltonian formalism in the dynamic regime using optical pulses that links waveguide optomechanics and cavity optomechanics, which can be used in the classical and quantum regime including quantum noise. Based on our formalism, a closed solution for coupled-mode equation under the undepleted assumption is provided and we found that the strong coupling regime is already accessible in current Brillouin waveguides by using pulses. We further investigate several possible experiments within waveguide optomechanics, including Brillouin-based coherent transfer, Brillouin cooling, and optoacoustic entanglement.

A new intermediate Hamiltonian Fock-space coupled-cluster formalism for the three-valence sector

The single-reference coupled-cluster (CC) method is one of the most efficient approaches for describing electron correlation effects in atoms and molecules but its successful application is limited to states dominated by a single Slater determinant. In cases where several determinants dominate the wave function expansion, the multi-reference (MR) CC formulations are required. They usually use the effective Hamiltonian formalism which allows dealing with two types of electron correlation appearing in the MR cases: nondynamic and dynamic. There are two MR-CC formulations of this type: the Hilbert space CC method and the Fock-space (FS) one. In the paper, a version of the FS-CC method designated for the description of systems with three-valence electrons is being considered. The idea of the intermediate Hamiltonian (IH) reformulation of the standard FS-CC method, which simplifies the calculations and avoids the intruder state problem, is discussed in this context. A new IH-FS-CC approach is presented which takes advantage of the redefinition of the normal ordering of the FS cluster expansion introduced by Lindgren. The redefinition significantly simplifies the IH-FS-CC formalism and lowers the computational cost of the calculations. The advantages of the new IH formulation are discussed in detail for the case of the FS-CC method in which the lowest-order cluster operators are included in all sectors of the Fock-space, including the three-valence one.

A Quantum State Scenario for Biological Self-Replication

With the prevalent conception of self-replication (SR, a hallmark of living systems) as a non-equilibrium process subject to thermodynamic laws, a complementary approach derives the low energy quantum states arising from a Hamiltonian that appears to be specific for bio-systems by its containing some strongly binding terms. The bindings attract properties of the template (T) and the reactants to form a replicate (R). The criterion for SR that emerges from the theory is that second order (bi-linear) interaction terms between degrees of motion of T-R and the thermal bath dominate negatively over a linear self-energy term, and thereby provide a binding between the attributes of T and R. The formalism (reminiscent of the Kramers-Anderson mechanism for superexchange) is from first principles, but hinges on a drastic simplification by modelling the T, R and bath variables on interacting qubits and by congesting the attraction into a single (control) parameter. The development relies on further simplifying features, such as Random Phase Approximations and an Effective Hamiltonian formalism. The entropic balance to replication is considered and found to reside in the far surroundings.

Mixed quantum-classical approach to model non-adiabatic electron-nuclear dynamics: Detailed balance and improved surface hopping method.

We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional "virtual" nuclear wave packets whose interference with the "real" (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phase shifts lead to the detailed balance condition in the strong decoherence limit.

The electronic spectrum of AgI2. Ab initio benchmark CASSCF + Averaged Coupled Pair Functional studies on the ligand-field states including spin-orbit couplings

The X2Πg, 2Σg+ and 2Δg states of AgI2 have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) calculations using especially developed valence basis sets to study the transition energies and equilibrium geometries. The spin–orbit (SO) effects were included through the effective Hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. AgI2 is a linear centrosymmetric molecule with a 2Πg ground state, in contradiction with ligand-field theory. The ACPF adiabatic excitation energies of the 2Σg+ and 2Δg states are 7344 and 26085 cm−1, respectively. A comparison of the present results with the previous ones for AgCl2 and AgBr2 shows a monotonic increase in the 2Πg-2Σg+ and 2Πg-2Δg transition energies due to a decrease of the ionic structures in the LF states as the atomic number of the halogen grows. The inclusion of the SO effects leads to a pure Ω = 3/2 X(2Πg) ground state, a Ω = 1/2 (83% 2Πg + 17% 2Σg+) A state, a Ω = 1/2 (17% 2Πg + 83% 2Σg+) B state, a Ω = 5/2 (2Δg) C state and a Ω = 3/2 (2Δg) D state. The X-A, X-B, X-C, X-D vertical transition energies are 4250, 11248, 27,127 and 30441 cm−1, respectively, nearly identical to the adiabatic Te values.

Design Algorithms of Driving-Induced Nonreciprocal Components

We utilize an effective Hamiltonian formalism, within the Floquet scattering framework, to design a class of driving-induced non-reciprocal components with {\it minimal} complexity. In the high driving-frequency limit, where our scheme is formally applicable, these designs demonstrate a leading order non-reciprocal performance which is inverse proportional to the driving frequency. Surprisingly, the optimal non-reciprocal behavior persists also in the slow driving regime. Our approach highlights the importance of physical loops in the design of these driven non-reciprocal components.

Negative-Differential-Resistance Devices Achieved by Band-Structure Engineering in Silicene under Periodic Potentials

In terms of band-gap engineering for devices, despite silicene's great promise, it has received considerably less attention than its carbon cousin graphene. Taking advantage of its tunable band gap, the authors use an effective Hamiltonian formalism to examine the formation of silicene superlattices. They theoretically consider engineering of the local band structure of silicene through application of an out-of-plane electric field, together with control over the spin and valley degrees of freedom, and finally show how to optimize negative differential resistance. This design principle could be extended to stacks of other two-dimensional materials as well.

Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field.

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism.

This paper presents a rigorous state-specific multi-reference coupled cluster formulation of the method first proposed by Meller et al. [J. Chem. Phys. 104, 4068 (1996)]. Guess values of the amplitudes of the single and double excitations (the T operator) on the top of the references are extracted from the knowledge of the coefficients of the Multi-Reference Singles and Doubles Configuration Interaction (MR-CISD) matrix. The multiple parentage problem is solved by scaling these amplitudes from the interaction between the references and the singles and doubles. Then one proceeds to a dressing of the MR-CISD matrix under the effect of the triples and quadruples, the coefficients of which are estimated from the action of exp(T). This dressing follows the logic of the intermediate effective Hamiltonian formalism. The dressed MR-CISD matrix is diagonalized and the process is iterated to convergence. As a simplification, the coefficients of the triples and quadruples may in practice be calculated from the action of T(2) only, introducing 5th-order differences in the energies. The so-simplified method is tested on a series of benchmark systems from Complete Active Spaces (CASs) involving 2-6 active electrons up to bond breakings. The comparison with full configuration interaction results shows that the errors are of the order of a few millihartree, five times smaller than those of the CAS-CISD, and the deviation to strict separability is lower than 10 μ hartree. The method is totally uncontracted, parallelizable, and extremely flexible since it may be applied to selected MR and/or selected CISD. Some potential generalizations are briefly discussed.

Engineering resonance dynamics of plasmon hybridized systems

The ability to control resonances is crucial in advancing applications of plasmonics ranging from chemical and biological sensing at the single molecule level to on-chip communication via fully optical interconnects. To this end, a method employing an effective Hamiltonian formalism is described to study and tailor resonances of plasmonic systems at optical frequencies. Using this method, we compute the complex poles of the scattering matrix and investigate resonance dynamics of coupled plasmonic bars. We show that symmetry breaking, by tailoring near-field interactions in the whole complex plane, provides a very large degree of tunability, including a controllable negative coupling regime.

Dc Josephson current in a long multichannel quantum wire

The dc Josephson current across a multi-channel SNS junction is computed by summing contributions from sub-gap Andreev bound states, as well as from continuum states propagating within the superconducting leads. We show that, in a long multi-channel SNS-junction, at low temperatures, all these contributions add up, so that the current can be entirely expressed in terms of single-particle normal- and Andreev reflection amplitudes at the Fermi level at both SN interfaces. Our derivation applies to a generic number of channels in the normal region and/or in the superconducting leads, without assumptions about scattering processes at the SN interfaces: if the channels within the central region have the same dispersion relation, it leads to simple analytical formulas for the current at low temperatures; if the channels within the central region have different dispersion relations, it allows for expressing the current in terms of a simple integral involving only scattering amplitudes at the Fermi level. Our result motivates using a low energy effective boundary Hamiltonian formalism for computing the current, which is crucial for treating Luttinger liquid interaction effects.

Microwave experiments using open chaotic cavities in the realm of the effective Hamiltonian formalism

AbstractThe description of open quantum system successfully uses the concept of the effective Hamiltonian, which takes into account the coupling to the environment. The concept can be extended to classical waves. Experimentally, classical waves are very convenient as they allow to control boundaries, coupling and absorption. We combine here recent works with microwaves investigating properties of open systems which can be described by an effective Hamiltonian. This ranges from spectral properties like modifications to level dynamics, width distribution and coupling fidelity to spatial properties like intensity distributions and complexness parameter which describes the non‐orthogonality of eigenfunctions.

The electronic spectrum of AgBr2: Ab initio benchmark calculations on the 2Πu and 2Σu+ charge transfer states including spin‐orbit effects

AbstractThe 2Πu and 2Σu+ charge transfer (CT) states of AgBr2 have been studied through benchmark ab initio HF, complete active space SCF, CASPT2, NEVPT2, and averaged coupled pair functional (ACPF) multireference calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, and Mulliken charges. The spin‐orbit (SO) effects have been included through the effective Hamiltonian formalism using the ACPF energies as |ΛSΣ> diagonal elements. The equilibrium Ag–Br distance for both CT states is larger than that of the X2Πg ground state. The ACPF adiabatic excitation energies of the 2Πu and 2Σu+ states are 4620 and 7006 cm‐1, respectively. Using previous ACPF benchmark studies showing that the 2Δg ligand field (LF) state lies more than 20,000 cm‐1 above the ground state, these new results lead to the following energetic ordering for the five lowest electronic states of AgBr2: X2Πg, 2Σg+, 2Πu, 2Σu+, and 2Δg, in sharp contradiction with Hartree–Fock theory. When considering the coupling of the LF and CT states, the inclusion of the SO effects leads to a pure Ω = 3/2 (X2Πg) ground state, Ω = 1/2 (92% 2Πg + 8% 2Σg+) A state, Ω = 3/2 (pure 2Πu) B state, Ω = 1/2 (68% 2Πu+32% 2Σu+) C state, Ω = 1/2 (8% 2Πg + 92% 2Σg+) D state, and an Ω = 1/2 (32% 2Πu + 68% 2Σu+) E state. We present here what we consider the most complete and accurate account of the electronic spectrum of AgBr2. © 2012 Wiley Periodicals, Inc.

Cosmic rays and tests of fundamental principles

It is now widely acknowledged that cosmic rays experiments can test possible new physics directly generated at the Planck scale or at some other fundamental scale. By studying particle properties at energies far beyond the reach of any man-made accelerator, they can yield unique checks of basic principles. A well-known example is provided by possible tests of special relativity at the highest cosmic-ray energies. But other essential ingredients of standard theories can in principle be tested: quantum mechanics, uncertainty principle, energy and momentum conservation, effective space-time dimensions, hamiltonian and lagrangian formalisms, postulates of cosmology, vacuum dynamics and particle propagation, quark and gluon confinement, elementariness of particles... Standard particle physics or string-like patterns may have a composite origin able to manifest itself through specific cosmic-ray signatures. Ultra-high energy cosmic rays, but also cosmic rays at lower energies, are probes of both "conventional" and new Physics. Status, prospects, new ideas, and open questions in the field are discussed. The Post Scriptum shows that several basic features of modern cosmology naturally appear in a SU(2) spinorial description of space-time without any need for matter, relativity or standard gravitation. New possible effects related to the spinorial space-time structure can also be foreseen. Similarly, the existence of spin-1/2 particles can be naturally related to physics beyond Planck scale and to a possible pre-Big Bang era.

Second-order state-specific multireference Møller Plesset perturbation theory: Application to energy surfaces of diimide, ethylene, butadiene, and cyclobutadiene

The complete active space spin-free state-specific multireference Møller-Plesset perturbation theory (SS-MRMPPT) based on the Rayleigh-Schrödinger expansion has proved to be very successful in describing electronic states of model and real molecular systems with predictive accuracy. The SS-MRMPPT method (which deals with one state while using a multiconfigurational reference wave function) is designed to avoid intruder effects along with a balanced description of both dynamic and static correlations in a size-extensive manner, which allows us to produce accurate potential energy surfaces (PESs) with a correct shape in bond-breaking processes. The SS-MRMPPT method is size consistent when localized orbitals on each fragment are used. The intruder state(s) almost inevitably interfere when computing the PESs involving the breaking of genuine chemical bonds. In such situations, the traditional effective Hamiltonian formalism often goes down, so that no physically acceptable solution can be obtained. In this work, we continue our analysis of the SS-MRMPPT method for systems and phenomena that cannot be described either with the conventional single-reference approach or effective Hamiltonian-based traditional MR methods. In this article, we investigate whether the encouraging results we have obtained at the SS-MRMPPT level in the study of cis-trans isomerization of diimide (N2H2), ethylene (C2H4), and 1,3-butadiene (C4H6) carry over to the study of chemical reactions. The energy surfaces of the double-bond flipping interconversion of the two equivalent ground and two lowest singlet state structures of cyclobutadiene have also been studied. All results have been discussed and assessed by comparing with other state-of-the-art calculations and corresponding experimental data whenever available.

The electronic spectrum of AgBr 2: Ab initio benchmark vs. DFT calculations on the lowest ligand-field states including spin–orbit effects

The X 2Π g, 2Σ g + and 2Δ g states of AgBr 2 have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) and DFT calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges and spin densities. The spin–orbit (SO) effects were included through the effective hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. At the ACPF level, the ground state is 2Π g, in contradiction with ligand-field theory and Hartree–Fock results. The ACPF adiabatic excitation energies of the 2Σ g + and 2Δ g states are 3825 and 20 152 cm −1, respectively. The inclusion of the SO effects leads to a pure Ω = 3/2 ( 2Π g) ground state, a Ω = 1/2 (97% 2Π g + 3% 2Σ g +) A state, a Ω = 1/2 (3% 2Π g + 97% 2Σ g +) B state, a Ω = 5/2 ( 2Δ g) C state and a Ω = 3/2 (99% 2Δ g) D state. The B97, B3LYP and PBE0 functionals, which were shown to yield accurate transition energies for CuCl 2, overestimate the X 2Π g– 2Σ g + T e by around 25% but provide a qualitative energetic ordering in agreement with CASSCF and ACPF results. The nature of the bonding in the X 2Π g ground state is different from that of AgCl 2 since the Mulliken charge on the metal is 0.95 while the spin density is only 0.39. DFT strongly delocalizes the spin density providing even smaller values of around 0.13 on Ag not only for the ground state, but also for the 2Σ g + state.

Statistics of resonance states in open chaotic systems: A perturbative approach

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (nonorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of weakly overlapping resonances, we apply the random matrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian orthogonal ensemble, we reveal and discuss the role of spectral fluctuations.

Quasimodes of a chaotic elastic cavity with increasing local losses

We report noninvasive measurements of the complex field of elastic quasimodes of a silicon wafer with chaotic shape. The amplitude and phase spatial distribution of the flexural modes are directly obtained by Fourier transform of time measurements. We investigate the crossover from real mode to complex-valued quasimode, when absorption is progressively increased on one edge of the wafer. The complexness parameter, which characterizes the degree to which a resonance state is complex valued, is measured for nonoverlapping resonances, and is found to be proportional to the nonhomogeneous contribution to the line broadening of the resonance. A simple two-level model based on the effective Hamiltonian formalism supports our experimental results.

Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

Using an energy-independent non-Hermitian Hamiltonian approach to open systems, we fully describe transport through a sequence of potential barriers as external barriers are varied. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian model, a transition to a superradiant regime is shown to occur. Transport properties undergo a strong change at the superradiance transition, where the transmission is maximized and a drastic change in the structure of resonances is demonstrated. Finally, we analyze the effect of the superradiance transition in the Anderson localized regime.