Counting monster potentials

Abstract We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which — according to the ODE/IM correspondence — should correspond to excited states of the Quantum KdV model.We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials.This allows us to associate to each partition of N a unique monster potential with N roots, of which we compute the spectrum. As a consequence, we prove — up to a few mathematical technicalities — that, fixed an integer N , the number of monster potentials with N roots coincides with the number of integer partitions of N , which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.

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Excited-State Dynamics in the RNA Nucleotide Uridine 5’-Monophosphate Investigated by Femtosecond Broadband Transient Absorption Spectroscopy

10.26434/chemrxiv.7860023 ◽

2019 ◽

Author(s):

Matthew M. Brister ◽

Carlos Crespo-Hernández

Keyword(s):

Excited State ◽

Excited States ◽

Ground State ◽

Transient Absorption ◽

Electronic Energy ◽

Transient Absorption Spectroscopy ◽

Electronic Relaxation ◽

Vibrationally Excited ◽

Excited State Dynamics ◽

Π State

Damage to RNA from ultraviolet radiation induce chemical modifications to the nucleobases. Unraveling the excited states involved in these reactions is essential, but investigations aimed at understanding the electronic-energy relaxation pathways of the RNA nucleotide uridine 5’-monophosphate (UMP) have not received enough attention. In this Letter, the excited-state dynamics of UMP is investigated in aqueous solution. Excitation at 267 nm results in a trifurcation event that leads to the simultaneous population of the vibrationally-excited ground state, a longlived 1nOπ* state, and a receiver triplet state within 200 fs. The receiver state internally convert to the long-lived 3ππ* state in an ultrafast time scale. The results elucidate the electronic relaxation pathways and clarify earlier transient absorption experiments performed for uracil derivatives in solution. This mechanistic information is important because long-lived nπ* and ππ* excited states of both singlet and triplet multiplicities are thought to lead to the formation of harmful photoproducts.

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Charge Transfer Between CO22+ and Ar or Ne at Collision Energies 3-10 eV

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20030178 ◽

2003 ◽

Vol 68 (1) ◽

pp. 178-188 ◽

Cited By ~ 3

Author(s):

Libor Mrázek ◽

Ján Žabka ◽

Zdeněk Dolejšek ◽

Zdeněk Herman

Keyword(s):

Charge Transfer ◽

Excited States ◽

Ground State ◽

Scattering Method ◽

Translational Energy ◽

Centre Of Mass ◽

Energy Distributions ◽

Zener Model ◽

Beam Scattering ◽

Product Ions

The beam scattering method was used to investigate non-dissociative single-electron charge transfer between the molecular dication CO22+ and Ar or Ne at several collision energies between 3-10 eV (centre-of-mass, c.m.). Relative translational energy distributions of the product ions showed that in the reaction with Ar the CO2+ product was mainly formed in reactions of the ground state of the dication, CO22+(X3Σg-), leading to the excited states of the product CO2+(A2Πu) and CO2+(B2Σu+). In the reaction with Ne, the largest probability had the process from the reactant dication excited state CO22+(1Σg+) leading to the product ion ground state CO2+(X2Πg). Less probable were processes between the other excited states of the dication CO22+, (1∆g), (1Σu-), (3∆u), also leading to the product ion ground state CO2+(X2Πg). Using the Landau-Zener model of the reaction window, relative populations of the ground and excited states of the dication CO22+ in the reactant beam were roughly estimated as (X3Σg):(1∆g):(1Σg+):(1Σu-):(3∆u) = 1.0:0.6:0.5:0.25:0.25.

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Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

Journal of High Energy Physics ◽

10.1007/jhep12(2020)160 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Jiaju Zhang ◽

M.A. Rajabpour

Keyword(s):

Excited States ◽

Single Particle ◽

Renyi Entropy ◽

Rényi Entropy ◽

Large Momentum ◽

Particle State ◽

Two Dimensional ◽

Universal Form ◽

Conformal Field ◽

Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

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The Microwave Spectrum of 3,4-Dihydro-1,2-Pyran

Zeitschrift für Naturforschung A ◽

10.1515/zna-1985-0909 ◽

1985 ◽

Vol 40 (9) ◽

pp. 913-919

Author(s):

Juan Carlos López ◽

José L. Alonso

Keyword(s):

Dipole Moment ◽

Excited States ◽

Ground State ◽

Principal Axis ◽

Microwave Spectrum ◽

Average Intensity ◽

Ring Conformation ◽

Vibrationally Excited ◽

Rotational Constants ◽

Displacement Measurements

Abstract The rotational transitions of 3,4-dihydro-1,2-pyran in the ground state and six vibrationally excited states have been assigned. The rotational constants for the ground state (A = 5198.1847(24), B = 4747.8716(24) and C = 2710.9161(24) have been derived by fitting μa, μb and μc-type transitions. The dipole moment was determined from Stark displacement measurements to be 1.400(8) D with its principal axis components |μa| =1.240(2), |μb| = 0.588(10) and |μc| = 0.278(8) D. A model calculation to reproduce the ground state rotational constants indicates that the data are consistent with a twisted ring conformation. The average intensity ratio gives vibrational separations between the ground and excited states of the ring-bending and ring-twisting modes of ~ 178 and ~ 277 cm-1 respectively.

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Zur Berechnung der chemischen Verschiebung unter besonderer Berücksichtigung des paramagnetischen Terms / Attempts to the Calculation of the Chemical Shift with Especial Consideration of the Paramagnetic Term

Zeitschrift für Naturforschung A ◽

10.1515/zna-1977-1231 ◽

1977 ◽

Vol 32 (12) ◽

pp. 1541-1543

Author(s):

H. Sterk ◽

J. J. Suschnigg

Keyword(s):

Chemical Shift ◽

Excited States ◽

Ground State ◽

Energy Gap

Abstract Attempts to the Calculation of the Chemical Shift with Especial Consideration of the Paramagnetic Term The calculation of the paramagnetic term according to the Pople formalism of the chemical shift is expanded. The hitherto constant value of the energy gap between the ground state and the excited states is replaced by the value of the lowest lying excitation. This leads to a remarkably better differentiation of the paramagnetic terms of different compounds. The influence is shown on ethane, ethene and ethine.

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OPTICAL ABSORPTION SPECTRA OF ARSENIC AND PHOSPHORUS IN SILICON

Canadian Journal of Physics ◽

10.1139/p62-156 ◽

1962 ◽

Vol 40 (10) ◽

pp. 1480-1489 ◽

Cited By ~ 19

Author(s):

J. W. Bichard ◽

J. C. Giles

Keyword(s):

Optical Absorption ◽

Absorption Spectra ◽

Excited States ◽

Ground State ◽

Absorption Lines ◽

Full Width ◽

Optical Absorption Spectra ◽

Phosphorus Impurity ◽

Line Widths ◽

Phosphorus In Silicon

The optical absorption spectra of arsenic and phosphorus donor impurities in silicon have been studied under conditions of improved resolution. Absorption lines due to transitions from the impurity ground state to the excited states 2p0, 2p±, 3p0, 3p±, 4p0, 4 p±, and 5p0, and 5p± have been observed at 4.2° K. The relative intensities of some of these absorption lines are compared with existing experimental and theoretical estimates. The contribution of instrumental broadening to the observed line widths is assessed and natural line widths are estimated. The estimates indicate values for the natural line widths which are much less than those previously reported. For phosphorus impurity, the natural line widths are estimated to be less than 0.08 × 10−3 electron volts full width at half-maximum. The possibility of concentration broadening is discussed in connection with the arsenic data.

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