The Exact Wavefunction Factorization of a Vibronic Coupling System

We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally the nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation

Many-body effects in the excitation spectrum of weakly-interacting Bose-Einstein condensates in one-dimensional optical lattices

In this work, we study many-body excitations of Bose-Einstein condensates (BECs) trapped in periodic one-dimensional optical lattices. In particular, we investigate the impact of quantum depletion onto the structure of the low-energy spectrum and contrast the findings to the mean-field predictions of the Bogoliubov-de Gennes (BdG) equations. Accurate results for the many-body excited states are obtained by applying a linear-response theory atop the MCTDHB (multiconfigurational time-dependent Hartree method for bosons) equations of motion, termed LR-MCTDHB. We demonstrate for condensates in a triple well that even weak ground-state depletion of around $1\%$ leads to visible many-body effects in the low-energy spectrum which deviate substantially from the corresponding BdG spectrum. We further show that these effects also appear in larger systems with more lattice sites and particles, indicating the general necessity of a full many-body treatment

Many-body tunneling dynamics of Bose-Einstein condensates and vortex states in two spatial dimensions

In this work, we study the out-of-equilibrium many-body tunneling dynamics of a Bose-Einstein condensate in a two-dimensional radial double well. We investigate the impact of interparticle repulsion and compare the influence of angular momentum on the many-body tunneling dynamics. Accurate many-body dynamics are obtained by solving the full many-body Schr\"odinger equation. We demonstrate that macroscopic vortex states of definite total angular momentum indeed tunnel and that, even in the regime of weak repulsions, a many-body treatment is necessary to capture the correct tunneling dynamics. As a general rule, many-body effects set in at weaker interactions when the tunneling system carries angular momentum.Comment: 26 pages, 9 figure

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate for the first time the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed by a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs.Comment: 5+eps pages, 4 figure

Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

Use of Equivalent Hermitian Hamiltonian for PTPT-Symmetric Sinusoidal Optical Lattices

We show how the band structure and beam dynamics of non-Hermitian $PT$-symmetric sinusoidal optical lattices can be approached from the point of view of the equivalent Hermitian problem, obtained by an analytic continuation in the transverse spatial variable $x$. In this latter problem the eigenvalue equation reduces to the Mathieu equation, whose eigenfunctions and properties have been well studied. That being the case, the beam propagation, which parallels the time-development of the wave-function in quantum mechanics, can be calculated using the equivalent of the method of stationary states. We also discuss a model potential that interpolates between a sinusoidal and periodic square well potential, showing that some of the striking properties of the sinusoidal potential, in particular birefringence, become much less prominent as one goes away from the sinusoidal case.Comment: 11 pages, 8 figure

PENINGKATAN HASIL BELAJAR LOMPAT JAUH GAYA SCHNEPPER DENGAN PENERAPAN ALAT BANTU PEMBELAJARAN PADA SISWA KELAS VIII G SMP NEGERI 8 SURAKARTA TAHUN PELAJARAN 2015 / 2016

ABSTRAK Fahrudin Rizky Kusuma. PENINGKATAN HASIL BELAJAR LOMPAT JAUH GAYA SCHNEPPER DENGAN PENERAPKAN ALAT BANTU PEMBELAJARAN PADA SISWA KELAS VIII SMP NEGERI 8 SURAKARTA TAHUN AJARAN 2015/2016. Skripsi. Surakarta : Fakultas Keguruan dan Ilmu pendidikan Universitas Sebelas Maret Surakarta, Juni 2016. Tujuan penelitian ini adalah untuk meningkatkan hasil belajar lompat jauh gaya schnepper pada siswa kelas VIII G SMP Negeri 8 Surakarta Tahun Ajaran 2015/2016. Penelitian ini merupakan Penelitian Tindakan kelas (PTK). Penelitian ini dilaksanakan dalam dua siklus dengan setiap siklus terdiri dari dua pertemuan. Subjek penelitian ini adalah siswa kelas VIII G SMP Negeri 8 Surakarta yang berjumlah 26 siswa, 16 siswa perempuan dan 10 siswa laki-laki. Teknik pengumpulan data adalah dengan observasi, tes, dan dokumentasi. Validitas data menggunakan teknik triangulasi data. Analisis data menggunakan kualitatif dan Kuantitatif. Hasil Penelitian Pada prasiklus, hanya 9 siswa yang tuntas (34,62 %) dan 17 siswa lainnya belum tuntas (65,38 %). Pada siklus I diperoleh hasil belajar dengan siswa yang telah tuntas sebanyak 15 siswa (57,69%) dan 11 siswa masih belum tuntas (42,31%) dengan perolehan nilai rata-rata afektif (89,57%), psikomotor (76,53%) dan Kognitif (56,97%). Pada siklus II, diperoleh hasil belajar dengan siswa yang telah tuntas sebanyak 22 siswa (84,61%) dan 4 siswa masih belum tuntas (15,39%). Dengan perolehan nilai rata-rata afektif (92,84%), psikomotor (85,18%) dan Kognitif (83,17%). Berdasarkan hasil analisis dari siklus I & II tersebut menunjukkan bahwa terjadi peningkatan yang signifikan dan sesuai dengan target pencapaian. Simpulan penelitian ini adalah penerapan alat bantu pembelajaran dapat meningkatkan hasil belajar lompat jauh gaya schnepper pada siswa kelas VIII G SMP Negeri 8 Surakarta Tahun Ajaran 2015/2016. Kata Kunci : Hasil belajar, Lompat Jauh Gaya Schnepper, Penerapan Alat Bantu Pembelajaran ABSTRACT Fahrudin Rizky Kusuma. INCREASING THE RESULT OF LEARNING SCHNEPPER LONG JUMP STYLE BY APPLYING TEACHING AID FOR EIGHTH GRADERS OF SMP NEGERI 8 SURAKARTA AT 2015/2016. Skripsi. Surakarta: Faculty of Teacher Training and Education Sebelas Maret University. Jun, 2016. The purpose of this research was increasing the result of learning Schnepeer long jump style for eighth graders of SMP Negeri 8 Surakarta at 2015/2016. This research was Classroom Action Research (CAR). It executed into two cycles; in every cycle consists of two meetings. The subject was the Class G of eight graders of SMP Negeri 8 Surakarta, the number of students were 26 people, consists of 16 female and 10 male students. Techniques of data collection were observation, test, and documentation. The validity of data used triangulation. Data analysis used descriptive technic that based on qualitative analysis and percentage. The result of pre-cycle only 9 students were completed (34.62 %) and 17 students were not yet (65.38%). At the first cycle obtained the learning outcomes, 15 students were completed (57.69%) and 11 students were not yet (42.31%) with the average value of affective (89.57%), psychomotor (76.53%), and cognitive (56.97%). At the second cycle obtained the learning result, 22 students were completed (84.61%) and 4 students were not yet (15.39%). At the second cycle obtained the average value of affective (92.84%), psychomotor (85.18%), and cognitive (83.17%). Based on the analysis of first and second cycles, the analysis showed that there was significantly enhancement and appropriate with the target result. The conclusion was applying teaching aid could increase the result of learning schnepper long jump style for Class G of eight graders of SMP Negeri 8 Surakarta at 2015/2016. Keywords: Result of learning, Schnepper long jump style, applying teaching aid