Rare Gas Atoms Research Articles

What does it take to stabilize a naphthalene anion?

We investigate attachment of slow electrons (0-10eV) to naphthalene (Np) clusters in a crossed beam experiment. Supersonic expansions under different conditions using different buffer gases generate the clusters: in He, Ne, and low pressure Ar, neat (Np)N clusters are formed, while we also observe mixed clusters of naphthalene with rare-gas atoms in co-expansion with Ar above 0.5bar and with Kr. Negatively charged (Np)n- and Rgm(Np)n- (Rg = Ar, Kr) clusters are analyzed by mass spectrometry, and electron energy dependent ion yields are measured. We show that the smallest stable naphthalene complex with an excess electron, the dimer (Np)2- anion, cannot be formed in a binary collision of a free electron with (Np)2 dimer, nor with (Np)3 trimer. Evaporation of a weakly bound Ar atom(s) from a mixed ArM(Np)2 cluster following electron attachment leads to the dimer (Np)2- anion. Larger (Np)n-, n > 3, transient cluster anions decay via evaporation of an Np unit on a timescale of tens of microseconds. The self-scavenging process opens around 6eV, where a naphthalene unit is electronically excited by the incoming electron, which is slowed down and trapped. However, the transient negative ion is efficiently stabilized only in the mixed clusters, from which Ar atom(s) can be evaporated.

Imaging Spin-Orbit Excitation of Yttrium through High-Energy Collisions with Rare Gas Atoms.

The energy required for spin-orbit excitation plays a critical role in understanding translational-to-electronic energy conversion, particularly in chemical reactions involving changes in spin states. This is particularly important for transition metal atoms possessing d-orbitals, which result in multiple spin-orbit split energy levels at low energies. The accurate identification and characterization of spin-orbit transitions in such species require advanced experimental techniques and theoretical support. In this study, the spin-orbit excited collisions of Y(2D3/2) with rare gas atoms Ne, Ar, and Kr leading to Y(2D5/2) were observed using laser-ablated crossed-beam and time-sliced ion velocity mapping imaging techniques. Through a comparison of the forward angular distributions of Y(2D3/2) to the backward and sideway scattering distributions of Y(2D5/2) from elastic and inelastic collisions of Y(2D) with rare gas atoms, this study reveals that the spin-orbit electronic excitation occurs with high collision energy and low impact parameters from backward and sideway collisions. The effectiveness of the spin-orbit excitation process is strongly dependent on the collision energy or temperature, suggesting that energy requirements of the process have to be considered in chemical reactions involving changes in spin states.

Collision of rare-gas atoms on helium nanodroplets: Theoretical evidence for an efficient coagulation of heavy rare-gas atoms.

The coagulation of rare-gas atoms (RG = Ne, Ar, Kr, Xe, and Rn) in helium nanodroplets (HNDs) composed of 1000 atoms is investigated by zero-point averaged dynamics where a He-He pseudopotential is used to make the droplet liquid with proper energies. This method reproduces the qualitative abundances of embedded Arn+1 structures obtained by Time-Dependent Density Functional Theory and Ring Polymer Molecular Dynamics for Ar + ArnHe1000 collisions at realistic projectile speeds and impact parameters. More generally, coagulation is found to be much more efficient for heavy rare-gases (Xe and Rn) than for light ones (Ne and Ar), a behavior mainly attributed to a slower energy dissipation of the projectile in the HND. When coagulation does not occur, the projectile maintains a speed of 10-30m s-1 within the HND, but its velocity vector is rarely oriented toward the dopant, and the projectile roams in a limited region of the droplet. The structure of embedded RGn+1 clusters does not systematically match their gas-phase global minimum structure, and more than 30% of RGn-RG unbound structures are due to one He atom located in between the projectile and a dopant atom.

Theoretical Study of Ground-State Barium-Rare Gas Van der Waals Complexes: Combining Rule Modeling and Ab Initio Calculations.

The present study aims to generate the potential energy curves (PECs) and spectroscopic constants for barium alkaline earth (AE) atoms interacting with rare gas (RG) atoms (He, Ne, Ar, Kr, and Xe). The study focuses on investigating the van der Waals bonds that characterize the interactions between alkaline-earth metals and RG atoms, with a specific emphasis on employing the Tang and Toennies (TT) potential model, known to accurately describe such interactions. The TT potential model was employed in conjunction with combining rules to calculate its parameters, which include dispersion coefficients C 2n and Born-Mayer constants A and b. Additionally, we have conducted high-level ab initio calculations at the CCSD(T) level for all Ba-RG ground states. Obtained PECs from both methods have been used to evaluate the spectroscopic properties D e, R e, ωe, B e, and ωeχe. Our findings reveal that the derived spectroscopic constants from the TT model exhibit good agreement with the results obtained from CCSD(T) calculations and with other available theoretical studies. Furthermore, to gain insights into the relative differences among AE-RG species, we calculated the κ parameter for AE-RG and AE+-RG (AE = Sr, Ca, Mg, Ba; RG = He-Xe) complexes. It is found that except for the case of Ba-RG and Ba+-RG, the κ values within the same series, AE-RG and AE+-RG, are remarkably close to each other.

Hard X-ray operation of X-ray gas monitors at theEuropean XFEL.

X-ray gas monitors (XGMs) are operated at the European XFEL for non-invasive single-shot pulse energy measurements and average beam-position monitoring. The underlying measurement principle is the photo-ionization of rare gas atoms at low gas pressures and the detection of the photo-ions and photo-electrons created. These are essential for tuning and sustaining self-amplified spontaneous emission (SASE) operation, machine radiation safety, and sorting single-shot experimental data according to pulse energy. In this paper, the first results from XGM operation at photon energies up to 30 keV are presented, which are far beyond the original specification of this device. Here, the Huge Aperture MultiPlier (HAMP) is used for single-shot pulse energy measurements since the standard X-ray gas monitor detectors (XGMDs) do notprovide a sufficient signal-to-noise ratio, even at the highest operating gas pressures. A single-shot correlation coefficient of 0.98 is measured between consecutive XGMs operated with HAMP, which is as good as measuring with the standard XGMD detectors. An intra-train non-linearity of the HAMP signal is discovered, and operation parameters to mitigate this effect are studied. The upper repetition rate limit of HAMP operation at 2.25 MHz is also determined. Finally, the possibilities and limits for future XGM operation at photon energies up to 50 keV are discussed.

Theoretical Insights into the Vibrational Structure of Carbon Dioxide Rare-Gas Complexes.

Two new flexible-monomer two-body ab initio potential energy surfaces (PESs) for the neon and krypton van der Waals complexes with carbon dioxide were developed, extending our previous work on the Ar-CO2 molecule. The accuracy of the PESs was validated by their agreement with the vibrational spectrum of the rare-gas complexes. The intermolecular and intramolecular vibrational excitation energies were computed at the vibrational self-consistent field and vibrational configuration interaction levels of theory. Overall, the agreement between theory and experiment is excellent throughout the vibrational spectra. The observed slight splitting of the bending modes, resulting from their nondegeneracy in the complexes, is confirmed by our computations, and the results qualitatively agree with the experiment. The splitting increases with increasing polarizability of the rare-gas atom. Additionally, we explain a discrepancy in the mode assignment in the intermolecular region of the neon complex with our VCI character assignment.

Modeling of flowing gas diode pumped rare gas atoms laser

Diode-pumped rare gas lasers (DPRGLs) have the potential for high optical conversion efficiency and excellent beam quality, positioning them as promising candidates for directed energy lasers. This study proposes a semi-analytical model for a flowing gas diode-pumped rare gas laser considering the influence of temperature elevation resulting from increased pump power on the output. Furthermore, we explore the relationship between laser output power density and gas temperature with respect to gas flow velocity. The results of numerical simulation agree well with those of Rawlins et al.’s experiment. The model addresses the existing gap in DPRGL dynamic models by incorporating temperature considerations, emphasizing the crucial role of a gas flow device in achieving high-energy laser. With the best set of parameters, the output power of DPRGL reaches 100 kW/cm2, at pumping power density of 300 kW/cm2 and gas flow velocity of 140 m/s. Parameter optimization is helpful for design of a relatively high-power DPRGL system.

Vibrational energy transfer in ammonia-helium collisions.

While the rotational energy transfer of ammonia by rare gas atoms and hydrogen molecules has been the focus of many studies, little is known about its vibrational relaxation, even though transitions involving the umbrella bending mode have been observed in many astrophysical environments. Here we explore the vibrational relaxation of the umbrella mode of ammonia induced by collisions with helium atoms by means of the close-coupling method on an ab initio potential energy surface. We compute cross sections up to kinetic energies of 1500 cm-1 and rate coefficients up to a temperature of 300 K for vibrational, rotational, and inversion transitions involving the lowest two vibrational states. We show that vibrational relaxation is much less efficient than rotation-inversion relaxation, although the rate coefficients for vibrational relaxation strongly increase with the temperature. We also observe important differences for vibrationally-elastic transitions within the lowest two vibrational states, i.e., for rotation-inversion transitions. These are a direct consequence of the difference in the tunnelling splitting of the lowest inversion levels.

Analytical formula for multiple ionization cross sections of rare gas atoms by electron and positron impact

Analytical formula for multiple ionization cross sections of rare gas atoms by electron and positron impact

Unusual Dynamics and Vibrational Fingerprints of van der Waals Dimers Formed by Linear Molecules and Rare-Gas Atoms.

Detailed structural, dynamical, and vibrational analyses have been performed for systems composed of linear triatomic molecules solvated by a single rare-gas atom, He, Ne, or Ar. Among the chromophores of these van der Waals (vdW) dimers, there are four neutral molecules (CO2, CS2, N2O, and OCS) and six molecular cations (HHe2+, HNe2+, HAr2+, HHeNe+, HHeAr+, and HNeAr+), both of apolar and polar nature. Following the exploration of bonding preferences, high-level four-dimensional (4D) potential energy surfaces (PESs) have been developed for 24 vdW dimers, keeping the two intramonomer bond lengths fixed. For these 24 complexes, over 1500 bound vibrational states have been obtained via quasi-variational nuclear-motion computations, employing exact kinetic-energy operators together with the accurate 4D PESs and their 2D/3D cuts. The reduced-dimensional (2D to 4D) dimer models have been compared with full-dimensional (6D) ones in the cases of the neutral CO2·Ar and charged HHe2+·He dimers, corroborating the high accuracy of the 2D to 4D vibrational energies. The reduced-dimensional models suggest that (a) while the equilibrium structures are T-shaped and planar, the effective ground-state structures are nonplanar, (b) certain bound states belong to collinear molecular structures, even when they are not minima, (c) the vdW vibrations are heavily mixed and many states have amplitudes corresponding to both the T-shaped and collinear structures, (d) there are a few dimers, for which even some of the vdW fundamentals lie above the first dissociation limit, and (e) the vdW vibrations are almost fully decoupled from the intramonomer bending motion.

Ab initio interaction potentials of alkali metal (M = Na and K)–rare gas (Rg = He, Ne, Ar, Kr, Xe and Rn) complexes

Spectroscopic properties and potential energy curves of alkali metal (M = Na and K) – rare gas (Rg = He, Ne, Ar, Kr, Xe and Rn) van der Waals molecules in their ground states have been studied in detail using spin-restricted open-shell coupled cluster with single and double excitations and perturbative contribution of connected triple excitations (RCCSD(T)) methods. The core-valence correlation (CV) effect was found to be crucial for M-RG molecules containing heavy rare gas atoms. The electronic energies were corrected for the basis set superposition error (BSSE) using the counterpoise method. Energies were extrapolated to the complete basis set (CBS) limit using a two-point scheme. The permanent electric dipole moments, static electric dipole polarizabilities and long-range dispersion coefficients were also calculated. The computed spectroscopic constants, vibrational levels and rotational constants were reported for M-RG and good agreement with the available experimental and theoretical values were found.

Doped rare gas clusters up to completion of first solvation shell, CO2-(Rg)n, n = 3-17, Rg = Ar, Kr, Xe.

Spectra of rare gas atom clusters containing a single carbon dioxide molecule are observed using a tunable mid-infrared (4.3 µm) source to probe a pulsed slit jet supersonic expansion. There are relatively few previous detailed experimental results on such clusters. The assigned clusters include CO2-Arn with n = 3, 4, 6, 9, 10, 11, 12, 15, and 17, and CO2-Krn and CO2-Xen with n = 3, 4, and 5. Each spectrum has (at least) a partially resolved rotational structure, and each yields precise values for the shift of the CO2 vibrational frequency (ν3) induced by the nearby rare gas atoms, together with one or more rotational constants. These results are compared with theoretical predictions. The more readily assigned CO2-Arn species tend to be those with symmetric structures, and CO2-Ar17 represents completion of a highly symmetric (D5h) solvation shell. Those not assigned (e.g., n = 7 and 13) are probably also present in the observed spectra but with band structures that are not well-resolved and, thus, are not recognizable. The spectra of CO2-Ar9, CO2-Ar15, and CO2-Ar17 suggest the presence of sequences involving very low frequency (≈2cm-1) cluster vibrational modes, an interpretation which should be amenable to theoretical confirmation (or rejection).

Kinetics of Metastable Argon Optical Excitation and Gain in Ar/He Microplasmas.

The optically pumped rare-gas metastable laser is capable of high-intensity lasing on a broad range of near-infrared transitions for excited-state rare gas atoms (Ar*, Kr*, Ne*, Xe*) diluted in flowing He. The lasing action is generated by photoexcitation of the metastable atom to an upper state, followed by collisional energy transfer with He to a neighboring state and lasing back to the metastable state. The metastables are generated in a high-efficiency electric discharge at pressures of ∼0.4 to 1 atm. The diode-pumped rare-gas laser (DPRGL) is a chemically inert analogue to diode-pumped alkali laser (DPAL) systems, with similar optical and power scaling characteristics for high-energy laser applications. We used a continuous-wave linear microplasma array in Ar/He mixtures to produce Ar(1s5) (Paschen notation) metastables at number densities exceeding 1013 cm-3. The gain medium was optically pumped by both a narrow-line 1 W titanium-sapphire laser and a 30 W diode laser. Tunable diode laser absorption and gain spectroscopy determined Ar(1s5) number densities and small-signal gains up to ∼2.5 cm-1. Continuous-wave lasing was observed using the diode pump laser. The results were analyzed with a steady-state kinetics model relating the gain and the Ar(1s5) number density.

Laser-pulse characterization using strong-field autocorrelation patterns and random-forest-based machine learning

Building on the strategy presented in Opt. Lett. 47, 3992 (2022), we demonstrate an efficient alternative approach for the in situ characterization of ultrashort low-frequency laser pulses. In this context, we employ first-principles quantum-mechanical calculations to model the strong-field ionization of rare-gas atoms and produce autocorrelation patterns for a set of few-femtosecond near-infrared laser pulses. We explore the nonperturbative and nonlinear dependence of the autocorrelation patterns on the pulse characteristics and postulate an analytical function describing these patterns. For every laser pulse considered, we employ the parameters appearing in this analytical function, together with the underlying pulse parameters for supervised machine learning. Specifically, we use the random-forest technique for retrieving key laser pulse parameters from autocorrelation patterns produced via strong-field ionization. The current approach offers advantages for application to experimental data.

Asymptotically spin-forbidden optical transitions in quasimolecules

The results obtained recently on optical transitions that are induced in excited diatomic quasimolecules temporarily existing under thermal collisions of atoms of the Groups IIA and XII in the metastable atomic state 3P2 and rare gas atoms in the normal state 1S are summarized.

New rovibrational subbands of Ar-D<sub>2</sub>O complex in the D<sub>2</sub>O bending mode region

The intermolecular interactions involving the water molecule play important roles in many fields of physics, chemistry, and biology. High-resolution spectroscopy of Van der Waals complexes formed by a rare gas atom and a water molecule can provide a wealth of information about these intermolecular interactions. The precise experimental data can be used to test the accuracies and efficiencies of various theoretical methods of constructing the intermolecular potential energy surfaces and calculating the bound states. In this work, the high-resolution infrared absorption spectrum of the Ar-D<sub>2</sub>O complex in the <i>v</i><sub>2</sub> bending region of D<sub>2</sub>O is measured by using an external cavity quantum cascade laser. A segmented rapid-scan data acquisition method is employed. The Ar-D<sub>2</sub>O complex is generated in a slit supersonic jet expansion by passing Ar gas through a vessel containing liquid D<sub>2</sub>O. Four new rovibrational subbands are assigned in the spectral range of 1150–1190 cm<sup>–1</sup>, namely <inline-formula><tex-math id="M1">\begin{document}$\Sigma \left( {{0_{00}}, {v_2} = 1} \right) \leftarrow \Sigma \left( {{1_{11}}} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M1.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$\Sigma \left( {{0_{00}}, {v_2} = 1} \right) \leftarrow \Pi \left( {{1_{11}}} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M2.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$\Sigma \left( {{1_{01}}, {v_2} = 1} \right) \leftarrow \Pi \left( {{1_{10}}} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M3.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$\Sigma \left( {{1_{01}}, {v_2} = 1} \right) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M4.png"/></alternatives></inline-formula><inline-formula><tex-math id="Z-20221230153751">\begin{document}$\leftarrow \Pi \left( {{1_{01}}} \right) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_Z-20221230153751.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_Z-20221230153751.png"/></alternatives></inline-formula>. The first two subbands belong to the <i>otho</i>- species of Ar-D<sub>2</sub>O, while the latter two belong to the <i>para</i>- species. The observed rovibrational transitions together with the previously reported pure rotational spectra having the common lower vibrational sub-states are analyzed by a weighted least-squares fitting using a pseudo-diatomic effective Hamiltonian. An experimental error of 10 kHz for the far-infrared transitions and 0.001 cm<sup>–1</sup> for the infrared transitions are set in the global fitting when using Pickett’s program SPFIT, respectively. The molecular constants including vibrational substate energy, rotational and centrifugal distortion constants, and Coriolis coupling constant, are determined accurately. The previous results for the <inline-formula><tex-math id="M5">\begin{document}$\Pi \left( {{1_{11}}, {v_2} = 0} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M5.png"/></alternatives></inline-formula> substate are found to be likely incorrect. The energy of the <inline-formula><tex-math id="M6">\begin{document}$\Sigma \left( {{0_{00}}, {v_2} = 1} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M6.png"/></alternatives></inline-formula>and <inline-formula><tex-math id="M7">\begin{document}$\Sigma \left( {{1_{01}}, {v_2} = 1} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221728_M7.png"/></alternatives></inline-formula>substates are determined experimentally for the first time. The band origin of Ar-D<sub>2</sub>O in the D<sub>2</sub>O <i>v</i><sub>2</sub> bending mode region is determined to be 1177.92144(13) cm<sup>–1</sup>, which is a red shift about 0.458 cm<sup>–1</sup> compared with the head of D<sub>2</sub>O monomer. The experimental vibrational substate energy is compared with its theoretical value based on a four-dimensional intermolecular potential energy surface which includes the normal coordinate of the D<sub>2</sub>O <i>v</i><sub>2</sub> bending mode. The experimental and theoretical results are in good agreement with each other. But the calculated energy levels are generally higher than the experimental values, so, there is still much room for improving the theoretical calculations.

Electron correlation dynamics in atomic Kr excited by XUV pulses and controlled by NIR laser pulses of variable intensity

We have investigated the possibility to track and control correlation dynamics of valence electrons in krypton (Kr) initiated by the absorption of one extreme ultraviolet (XUV) photon. In this investigation, pump-probe experiments have been performed where monochromatized single high-harmonics at photon energies 29.6, 32.8, and 35.9 eV have been used as pump to populate different intermediate excited states. A temporally delayed near-infrared (NIR) pulse probes the population of various decay channels via the detection of Kr2+ ion yields and its transient profiles. We observe that by varying the NIR pulse intensity within a range from to W cm−2, the shape of the Kr2+ transient profile changes significantly. We show that by varying the intensity of the NIR pulse, it is possible—(i) to control the ratio between sequential and non-sequential double ionization of Kr; (ii) to selectively probe quantum beating oscillations between Kr satellite states that are coherently excited within the bandwidth of the XUV pulse; and (iii) to specifically probe the relaxation dynamics of doubly excited (Kr) decay channels. Our studies show that the contribution of different ionization and decay channels (i)–(iii) can be altered by the NIR pulse intensity, thus demonstrating an efficient way to control the ionization dynamics in rare gas atoms.

Pulsed-ramped-field-ionisation zero-kinetic-energy photoelectron spectroscopy of the metastable rare-gas atoms Ar, Kr and Xe.

The photoionisation of the metastable rare-gas atoms Rg = Ar, Kr and Xe is investigated at the Rg+ […](ns)2(np)5 2P3/2 ← Rg[…](ns)2(np)5((n + 1)s) 13P2 photoionisation threshold (n = 3, 4 and 5 for Ar, Kr and Xe) using the technique of pulsed-ramped-field-ionisation zero-kinetic-energy (PRFI-ZEKE) photoelectron spectroscopy. This technique, which monitors the field ionisation of high Rydberg states induced by a slowly growing electric-field ramp after a prepulse of opposite polarity, was recently introduced to record photoelectron spectra with high resolution and high sensitivity [Harper, Chen, Boyé-Péronne and Gans, Phys. Chem. Chem. Phys., 2022, 117, 9353]. A tunable UV laser system with a bandwidth of 30 MHz is used here to establish the factors determining the resolution and overall accuracy of this new method. In particular, the effects of stray electric fields, and of the magnitude of the prepulse and the field ramp on PRFI-ZEKE photoelectron spectra are studied by combining experiments with numerical simulations of the field-ionisation of high Rydberg states and of the electron flight times from the ionisation spot to the detector. A spectral resolution of 0.05 cm-1 is demonstrated in the photoelectron spectrum of metastable Ar.

Electron Correlations in Sequential Two-Photon Double Ionization of an Ar Atom

Sequential two-photon ionization is a process that is experimentally accessible due to the use of new free-electron laser sources for excitation. For the prototypical rare Ar gas atoms, a photoelectron spectrum (PES) corresponding to the second step of the sequential two-photon double ionization (2PDIII) at a photon excitation energy of 65.3 eV was studied theoretically with a focus on the consequences of electron correlations in the considered process. The calculation predicts many intense lines at low photoelectron energies, which cannot be explained on the basis of a one-electron approximation. The processes that lead to the appearance of these lines include many-electron correlations, either in the first or second step of photoionization. A significant fraction of the intensity of the low-energy part of PES is associated with the Auger decay of the excited states formed at the second step of 2PDI. The shape of the low-energy part of the 2PDIII PES is expected to be dependent on both the energy of photon excitations and the flux of the exciting beam.

Equilibrium and Non-Equilibrium Lattice Dynamics of Anharmonic Systems.

In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation-dissipation theorem and the Donsker-Furutsu-Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures.