Operator Spreading in Quantum Maps

Operators in ergodic spin-chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin-chains. Here we initiate the study of "operator spreading" in quantum maps on a torus, systems which do not have a tensor-product Hilbert space or a notion of spatial locality. Using the perturbed Arnold cat map as an example, we analytically compare and contrast the evolutions of functions on classical phase space and quantum operator evolutions, and identify distinct timescales that characterize the dynamics of operators in quantum chaotic maps. Until an Ehrenfest time, the quantum system exhibits classical chaos, i.e. it mimics the behavior of the corresponding classical system. After an operator scrambling time, the operator looks "random" in the initial basis, a characteristic feature of quantum chaos. These timescales can be related to the quasi-energy spectrum of the unitary via the spectral form factor. Furthermore, we show examples of "emergent classicality" in quantum problems far away from the classical limit. Finally, we study operator evolution in non-chaotic and mixed quantum maps using the Chirikov standard map as an example.Comment: 21 pages, 7 figures v2: References adde

A partial checklist of moths (Lepidoptera) of Dehradun, Mussoorie and Devalsari in Garhwal, Uttarakhand, India

Two-hundred-and-forty-eight species of moths were recorded during surveys conducted over 40 nights in Dehradun and Mussoorie in Dehradun District and Devalsari in Tehri Garhwal District in Uttarakhand.</p

Butterflies (Lepidoptera) of Chizami, Phek District, Nagaland, India

The butterflies of Chizami, Phek District of Nagaland, India were documented over a period of three years (2011–2014). This represents the first list of butterfly records from Nagaland after publications by Tytler between 1911 and 1914. Two-hundred-and-twelve (212) species were recorded of which 34 species are legally protected under various schedules of the Wildlife (Protection) Act, 1972. Amongst the many significant records during the survey, two species, the Tawny Emperor Chitoria ulupi ulupi and the Comic Oakblue Arhopala comica were recorded from India after a period of100 years.</span

Butterflies (Lepidoptera) of the Kameng Protected Area Complex, western Arunachal Pradesh, India

The butterflies of the Kameng Protected Area Complex in western Arunachal Pradesh, India, covering the protected areas of Eaglenest Wildlife Sanctuary, Pakke Tiger Reserve and Sessa Orchid Wildlife Sanctuary were surveyed over a 5-year period (2009–2014).  A total of 421 butterfly species were recorded during the survey, including two species new to India (Gonepteryx amintha thibetana and Bhutanitis ludlowi) and several species rediscoveries and range extensions in the Eastern Himalaya, most notably Arhopala belphoebe, Sovia separata magna, Aulocera saraswati vishnu, Calinaga aborica, Callerebia annada annada, and Callerebria scanda opima.  Here we provide an annotated checklist of butterflies of the Kameng Protected Area Complex, including historical records, distributions, abundance, habitats and other notes on these 421 species. An additional 42 species recorded in older literature or by other authors in recent times are also listed, taking the total number of species recorded in the landscape to 463.  </div

Butterflies of Garhwal, Uttarakhand, western Himalaya, India

Thirty percent of butterfly species that occur in India are found in the Garhwal region of the western Himalaya, which comprise six districts of Uttarakhand State with five major vegetation types lying between the catchments of the Ganga and Yamuna rivers.  The annotated checklist compiled here for this region comprises 407 species and takes into account all the species recorded since 1899, when the first list of 323 species was prepared by Mackinnon &amp; de Nicéville on the ‘butterflies of Mussoorie and its adjacent areas’.  Over a 20 year period (1986–1990; 2000–June 2015) the present authors maintained detailed notes and were able personally to record 349 species.  This information is presented in a checklist, together with details of the month, year and site of each record, relative abundance, Indian Wildlife (Protection) Act, 1972 (IWPA) status, as well as references of earlier records made by other authors in Garhwal for those species that the authors were not able to record themselves.  Forty-nine species recorded in the region have been placed under various schedules of IWPA; only one species, the Golden Emperor Dilipa morgiana Westwood, is listed in Schedule I Part IV, the others being mainly included under Schedule II Part II.  The paper also discusses new range extensions and significant records (past and present), identifies major biotic factors that threaten butterfly diversity in Garhwal, and suggests the scope for butterfly ecotourism in the state as an option for long term conservation.  </div

The sighting of Howarth’s Hairstreak (Lepidoptera: Lycaenidae: Theclinae: Chrysozephyrus disparatus interpositus Howarth, 1957) from Tenga Valley, Arunachal Pradesh, India, extending its known range

The butterfly subspecies, Chrysozephyrus disparatus interpositus is sighted at Tenga Valley, Western Arunachal Pradesh, 58 years after its original description, extending its known range eastwards by 350 km. </p

Re-discovery of Calinaga aborica Tytler, 1915 (Lepidoptera: Nymphalidae: Calinaginae) from Arunachal Pradesh, India

The butterfly Calinaga aborica Tytler, 1915 has been re-discovered a hundred years after its original description, and its range extended by 200km westwards into western Arunachal Pradesh, India.  </div