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Too familiar with Bose Hubbard model, but suddenly got stuck by a simple question: Why is the kinetic term (to be precise should be single body part) negative?
Questionasker said:Too familiar with Bose Hubbard model, but suddenly got stuck by a simple question: Why is the kinetic term (to be precise should be single body part) negative?
fzero said:The hopping term is not just the kinetic energy, but also includes the interaction of the particles with the lattice. If the interaction between the particles and the lattice sites is attractive, then often the energy spectrum will contain negative energy bound states (ignoring the other interactions, these are just the analogue of electrons being bound in atoms). Note that the hopping parameter (usually called ##t##) must still be specified. The - sign is usually chosen in the expectation that ##t>0##, but for a specific system, it might not be so.
Negative kinetic energy in Bose Hubbard mode refers to a phenomenon in which the kinetic energy of a Bose-Einstein condensate (BEC) in a periodic lattice potential becomes negative. This can occur when the BEC is in the Mott insulating phase, where the atoms are localized and the kinetic energy term in the Hamiltonian becomes negative due to the periodic potential.
Negative kinetic energy leads to a repulsive interaction between the atoms in the BEC, which can result in interesting dynamics such as the formation of bright solitons or the suppression of tunneling between lattice sites. It can also affect the stability and phase transitions of the BEC system.
Yes, negative kinetic energy in Bose Hubbard mode has been observed in experimental studies of BECs in optical lattices. By measuring the energy spectrum of the BEC, researchers can detect the negative kinetic energy term and its effects on the system.
Negative kinetic energy in Bose Hubbard mode has potential applications in quantum information processing and quantum simulation. By manipulating the BEC in the lattice, researchers can explore novel quantum phenomena and study complex systems that are difficult to simulate with classical computers.
Yes, there is ongoing research in this field, with scientists studying the effects of negative kinetic energy on BECs in different lattice geometries and exploring its potential applications. There is also interest in understanding the fundamental physics behind this phenomenon and its connections to other areas of physics, such as superfluidity and topological states of matter.